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Keywords:

  • large eddy simulation;
  • turbulent flow;
  • contaminant transport;
  • mass exchange processes;
  • dead zone models

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[1] Large eddy simulation is used to investigate the dynamics of the main coherent structures present in the flow around two vertical submerged groynes situated in a long flatbed open channel. The mass exchange processes between the embayment region and the main channel are investigated by studying the ejection of a contaminant introduced instantaneously inside the embayment. The instantaneous and mean structure of the horseshoe vortex system forming at the base of the upstream groyne and the bed shear distributions that determine the evolution of the scour in the groyne region are investigated. It is found that the amplification of the bed shear stress in the accelerating region around the tip of the upstream groyne is around one order of magnitude larger relative to the mean bed shear stress in the incoming flow. Analysis of the instantaneous flow fields shows that the eddies that are shed inside the horizontal and vertical detached shear layers play an important role in controlling the mass exchange at the lateral and roof interfaces. It is found that most of the pollutant leaves the embayment through the roof and bottom lateral sections. The overall mass exchange process is qualitatively different and substantially accelerated compared to the case when the groynes are emerged. However, it is shown that similar to the emerged case, the decay of the mass of contaminant within the embayment cannot be characterized by a unique value of the exchange coefficient used in simple dead zone theory models.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[2] Installing groynes in a river has important implications for controlling the scouring process along river banks, maintaining channels for navigation, restoring fish habitat and on the mass transport processes (e.g., suspended particulates and organic matter) throughout the channel [Uijttewaal, 2005]. Series of spur dikes are frequently used in middle and lower reaches of alluvial rivers. In many rivers flooding occurs several times a year causing most groynes to become submerged. The momentum convected into the embayment between successive groynes by the flow overtopping the groyne crest can significantly change the whole circulation pattern inside and around the embayments. Thus studying the effect of submergence on the momentum and mass transfer processes at groyne fields is important.

[3] The height of the groyne crest is usually chosen close to the yearly averaged water level in the river. As discussed by Uijttewaal [2005], a crest built too high can lead to an unnecessary high flow resistance at flood conditions, while a crest built too low decreases the capacity of the groynes to confine the flow at normal water levels. The height of the groyne crest can be thought of as a design parameter optimized to ensure the main functions of a groyne field. They include directing flow away from the river banks, constricting flow to increase scouring in the main channel for navigation purposes while limiting the local scour around the groyne tip, insuring the ability to pass a flood flow efficiently and enhancing the biodiversity of the vegetation and fish population in the river reach [see also Uijttewaal, 2005; Engelhardt et al., 2004].

[4] Compared to the flow around an emerged groyne field where the momentum and mass exchange take place only laterally at the interface between the embayment and the main channel, the hydrodynamics of the flow around a submerged groyne field is far more complicated as part of the flow advected toward the groyne region separates into an overflow that is advected over the groyne crest. The overflow exchanges momentum with the embayments through their roof interface. The coherent structures that populate the interfacial mixing layer at the lateral and roof interfaces control the exchange of mass and momentum. The velocity and pressure fluctuations inside the two mixing layers dominate the background turbulence and intensify the local three-dimensionality of the flow. Experiments [e.g., Uijttewaal, 2005] show that if the submergence is relatively high, the overtopping flow remains relatively parallel to the flow direction in the main channel near the free surface while inside the embayment strong recirculatory motions are present. The streamwise velocity over the roof interface is generally higher than the mean channel velocity and peaks as the overflow is advected over the crests of the groynes. The recirculatory motions present in the emerged case near the free surface, in particular the fairly two-dimensional (2-D) horizontal eddies observed in shallow embayments, are practically absent near the free surface at high submergence levels. If the submergence is relatively low, it is expected that in the deeper layers of the embayment the flow dynamics will be still determined to a great extent by the momentum exchange via the lateral mixing layer.

[5] A better understanding of the flow hydrodynamics and mass exchange processes in a groyne field will ultimately contribute to optimization of groyne design. One option to study these flows is to use numerical modeling techniques. Three-dimensional (3-D) effects associated with massive separation, strong interactions between the eddies in the mixing layers and the flow inside the embayment, the presence of unsteady vortex shedding and strong adverse pressure gradients require full 3-D nonhydrostatic simulations with advanced eddy-resolving techniques to accurately capture the complex flow and the dynamics of the large-scale turbulence around the groyne field region, especially in the submerged case.

[6] Eddy-resolving techniques like large eddy simulation (LES) are becoming more and more popular in river engineering applications. A good review of previous LES applications in river mechanics and fluvial geomorphic research is given by Keylock et al. [2005] along with an in depth description of recent trends in LES modeling and their suitability for river engineering applications. The role of coherent structures in open channel flows was investigated among others by Zedler and Street [2001], Tseng and Ferziger [2004], Stoesser et al. [2006b] who performed LES of flow over dunes of various shapes, and by Cui et al. [2003] who conducted LES of open channel flow over 2-D bottom ribs. Recently, LES of open channel flow over rough surfaces containing two layers of spheres was conducted by Stoesser and Rodi [2006]. Flow over ripples in oscillatory flow was studied using LES by Chang and Scotti [2004] and by Zedler and Street [2006]. Flow in a channel with a bottom cavity containing neutrally buoyant fluid/contaminant or negatively buoyant fluid (e.g., salt water)/contaminant, and the ejection of the contaminant from the bottom cavity were studied using LES by Kirkpatrick and Armfield [2005] and by Chang et al. [2006, 2007a, 2007b]. Flow in an open channel with bottom roughness due to the presence of vertical submerged plant stems (submerged vegetation) was studied using LES by Stoesser et al. [2006a]. Related to flow in or around typical hydraulic structures present in rivers, recent applications include the LES simulation of the flow in a water pump intake of realistic geometry by Tokyay and Constantinescu [2006], the detached eddy simulation [DES] simulation of flow past a bridge abutment in an open channel with flat bed by Paik et al. [2004], the LES simulation of flow past a circular bridge pier in an open channel with deformed bed corresponding to equilibrium scour conditions by Kirkil et al. [2006] and the LES simulation of flow past two emerged groynes (see Figure 1) mounted on one of the lateral walls of a straight channel by McCoy et al. [2006a]. The flow through river channel confluences with significant bed discordance was calculated using LES by Bradbrook et al. [2000, 2001].

image

Figure 1. General sketch showing channel flow with two emerged groynes.

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[7] LES is used in the present paper to study the flow and mass exchange processes around a generic geometry containing two submerged groynes (one embayment) in a flatbed open channel with vertical lateral walls (Figure 2a). The interest in this flow is motivated by its similarity to flow around groynes in natural rivers. The ratio of the embayment length over width is close to two which is typical of many river groyne fields [Uijttewaal et al., 2001; Engelhardt et al., 2004]. This simplified geometry retains some of the main characteristics and challenges of the flow past a series of embayments while requiring a lesser amount of computational resources to sufficiently resolve the flow using LES without wall functions. This type of configuration was studied experimentally and numerically using RANS models for the emerged and/or submerged cases by Chen and Ikeda [1997], Tominaga et al. [2000, 2001a, 2001b] and Kimura et al. [2003]. The investigation by Kimura et al. [2003] also considered the effect of the angle between the groynes and the channel.

image

Figure 2. General sketch showing channel flow with two submerged groynes. (a) Geometry and main flow features. (b) Position of the planes where solution is analyzed.

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[8] Though the Reynolds number at which this investigation is conducted is relatively low (Reh = Uh/ν = 19,000, where U is the bulk channel velocity, h is the channel depth, ν is the molecular viscosity) because of the fact that in the present simulation the incoming flow is fully turbulent and the main characteristics of the coherent structures present in fully turbulent channel flows are relatively independent of the Reynolds number, one expects the flow physics to be similar to that observed at much higher Reynolds numbers encountered in river reaches. The Reynolds number in the present investigation is in the typical range at which laboratory model studies of flow around groyne fields are conducted. Related to scour phenomena at groyne fields, which are one of the most important factors in the design of these structures, it is observed that the strongest erosion occurs for most groyne designs around the first groyne regardless of the number of groynes in the field. Though scale effects may influence the strength of the HV system, experimental investigations (e.g., see review by Simpson [2001]) show that the turbulent HV system at the base of surface mounted bluff bodies is present at very large Reynolds numbers in the range corresponding to field scale for river groynes. As the flow pattern around the first groyne is expected to be similar in the present configuration containing only one embayment and in configurations containing multiple embayments, results obtained in the present study can be used to better understand the structure of the horseshoe vortex (HV) system around the most upstream groyne in a series at the initiation of the scour process.

[9] Specific objectives include: (1) visualizing and understanding the interaction among the main large-scale flow structures present in the region around the groynes and their role in the mass exchange between channel and embayment, (2) studying the structure of the HV system at the base of the upstream groyne and its effect on the bed shear stress distribution and eventually on the bed morphology changes, (3) quantifying the exchange of dissolved matter between the embayment and the main channel, (4) understanding how mixing takes place over the embayment depth, (5) estimating on the basis of LES results the mass exchange coefficients used in simple mass exchange models based on dead zone theory, and (6) understanding the differences between the emerged and submerged cases.

2. Background

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[10] Several researchers have investigated the effects of submergence on groyne field hydrodynamics, single spur dikes, barbs, etc. The ratio of the total channel depth, h, to the groyne height, D, is called relative submergence. It is the main parameter distinguishing among cases of varying submergence. In most scaled laboratory experiments the channel Reynolds number was typically in the range of 5,000 to 50,000 and the incoming flow was fully turbulent.

[11] Uijttewaal [2005] studied experimentally the effects of submergence on the mean flow field, recirculation patterns, intensity of vortex shedding in the mixing layer, and time-dependent fluctuations for a multiple embayment configuration representative of groyne fields encountered in large European rivers. Velocities were measured in a 1:40 scaled model at the free surface using particle tracking velocimetry (PTV). Two levels of relative submergence were examined, 1.16, 1.28 and several groyne designs were examined. Overall, the effect of groyne submergence made the flow more complex and dominated by strong 3-D effects. In some of the test cases considered (relatively low submergence depth) it was observed that the momentum that enters the groyne field via the vertical mixing layer can interrupt the recirculating pattern within the groyne field typically observed in the emerged case. The flow inside the groyne field then becomes relatively parallel to the flow in the main channel and after a while shifts back to a recirculating pattern until another strong overtopping event occurs. Compared to the emerged case, substantially higher velocities are present in the upper layers of the groyne field. Also, it was observed that strong eddies were advected into the mixing layer originating at the groyne crest. The author concludes that for simulation of submerged groynes a fully 3-D LES model is needed to represent the complex 3-D flow behavior.

[12] In a related study of a similar configuration, Yossef and Uijttewaal [2003] collected velocity data using electromagnetic flowmeters and PTV. The flow pattern in the relatively low submergence case was found to alternate between the overtopping flow and the lateral flow being dominant in the embayment region. The time series showed that large-scale velocity fluctuations were present in all the cases but the turbulence characteristics in the submerged case were considerably different than those in the emerged case. The width of the horizontal mixing layer was found to be larger in the submerged case.

[13] Tominaga et al. [2001b] investigated the effect of relative submergence on the flow near a series of two groynes utilizing particle image velocimetry (PIV). Measurements were made in several vertical and horizontal planes. The presence of strong vortices shed from the first groyne parallel to the lateral and roof interfaces of the embayment was observed. The deflection of the horizontal DSL became larger with the increase of the relative height of the groyne. Compared to the emerged case, the momentum and mass exchange were observed to be larger in the submerged cases. For relative submergence depths less then two, a large increase of the inflow velocities in the region upstream of the second dike and of the outflow velocities in the region downstream of the first groyne were observed at the two interfaces. Consistent with other experimental investigations, the vortical structures were strengthened and the mass exchange was more intense in the submerged cases.

[14] Several studies of flow around groyne fields tried to estimate the temporal mass decay associated with ejection of a contaminant introduced instantaneously in one or several embayments. In these experiments [e.g., Uijttewaal et al., 2001; Weitbrecht et al., 2003; Kurtze et al., 2002] colored dye was used to simulate the dispersion of a passive contaminant. A gray scale analysis method was used to calculate the time-dependent depth-averaged dye concentrations for measurements of the temporal variation of the mass of contaminant within the embayment and to estimate global exchange coefficients. One limitation of these methods is that in the case of a submerged embayment it cannot separate between the dye within and above the embayment. Engelhardt et al. [2004] performed a field study of the flow structure and characteristics of mixing in a river reach with irregular groynes and complex bathymetry. In their investigation, the mass decay was estimated using three-component acoustic Doppler velocity meter (ADV) measurements inside the embayment coupled with a numerical random walk model to mimic the behavior of a tracer particle within a fluid. The numerical tracer was dispersed uniformly over the embayment volume and the trajectories of the particles were recorded over several hours. On the basis of this information, the time variation of the mean concentration of the particles within the embayment volume was estimated.

[15] Most of these investigations provided a detailed analysis of the flow and turbulence characteristics at the free surface. Some of them estimated the global exchange rates between embayment and channel. However, a 3-D characterization of the mass exchange process and its vertical nonuniformity is still lacking mainly because the experimental methods measuring mean dye concentration do not provide any quantitative information on the variation of the dye concentration over the embayment depth. This is especially important for submerged configurations. Also there is practically no quantitative information from these studies on the bed shear stress and pressure fluctuations distributions in the near bed region that determine the evolution of the sediment transport and local scour phenomena.

[16] The case of the flow past single and multiple submerged groynes was studied by means of 3-D simulations using several RANS models by Peng and Kawahara [1997] and Peng et al. [1999a]. In the case of an isolated submerged groyne, the size of the downstream recirculation region was found to decrease in the vertical direction with the distance from the bed. They found that although the simulations, especially the one using a nonlinear model, were able to capture some of the main flow features observed in experiments, all the RANS models underpredicted the velocity in the tip region of the spur dike and near the opposite sidewall of the groyne field. The same group [Peng et al., 1999b] performed RANS simulations of the flow around single and multiple groynes with a loose bed. The sediment transport model accounted for gravitational bed slope effects and used the Meyer-Peter-Muller formula to calculate the bed load transport rate. The bed elevation was calculated from the continuity equation for the 2-D sediment transport. The local scour and deposition patterns around submerged spur dikes were calculated and compared with experimental data. The location and magnitude of the maximum scour depth near the groyne nose were reproduced reasonably well although the pattern of local scour and deposition showed some differences with the experiment.

[17] A 2-D depth-averaged numerical model (Delft3D-FLOW) utilizing horizontal LES (HLES) was applied to predict the flow past an array of groynes with a fixed bed by Uijttewaal and van Schijndel [2004]. Both the emerged and submerged cases were considered. To model the effect of the submergence on the groynes, an additional local roughness was added to the model. The flow separation and the areas of high turbulence intensity were better reproduced by HLES compared to results obtained using the k-ɛ model. The model predictions for the submerged case were poorer than those obtained for the emerged case. It was concluded that the high three-dimensionality of the flow in the submerged case limited the applicability of a 2-D depth-averaged model. A similar model was used by Yossef and Klaassen [2002] to predict flow and bathymetry evolution in a channel with groynes disposed on both sides of the channel. The model captured some of the qualitative features of the bed scouring around groynes observed in experiments.

[18] Fully 3-D nonhydrostatic LES simulations were recently reported by Hinterberger [2004] and McCoy et al. [2006a, 2006b]. In these studies the case of emerged groynes was considered, the meshes were fine enough to capture the dynamics of the energetic structures, the channel Reynolds number was around 104 and the mass exchange processes were studied by considering the ejection of a passive scalar introduced instantaneously inside the embayment volume. In the study by Hinterberger [2004] a periodic boundary condition was used in the streamwise direction corresponding to an infinite array of groynes. In the second study the case of an isolated embayment was considered while in the third one the case of a finite series of groynes was considered. These studies allowed a detailed investigation of the instantaneous and mean flow patterns and of the role of coherent structures in the mass exchange process in the case of emerged groynes. The present study considers the same geometrical (see Figure 1) and flow parameters as the ones used by McCoy et al. [2006a] except for the channel height that is now taken to be 1.4 times the height of the groynes (see Figure 2a).

3. Numerical Solver and LES Model

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[19] The numerical solver utilized to perform the present simulations is a massively parallel LES code [Mahesh et al., 2004, 2006]. It can employ hybrid unstructured meshes that allow for simulating flows in very complex geometries. The algorithm discretely conserves energy. This makes high Reynolds number simulations possible without use of numerical dissipation in the momentum equations. An advection-diffusion equation is solved for the nondimensional concentration C (0 < C < 1) of a passive contaminant. All operators in the finite volume formulation of the Navier-Stokes equations are discretized using central schemes including the convective ones. A collocated, fractional step scheme is used to solve the filtered Navier-Stokes equations. The convective and viscous operators in the momentum (predictor step) and scalar transport equations are discretized in time using the (implicit) Crank Nicholson scheme. After the governing equations are discretized in time, the discrete momentum and scalar transport equations are solved using the successive overrelaxation (SOR) method. The discretized pressure equation is solved using conjugate gradient method with preconditioning.

[20] The filtered continuity, momentum and scalar transport equations are

  • equation image
  • equation image
  • equation image

[21] As implicit filtering is used, ui refers to the grid filtered (resolved) velocity component in the ‘i’ direction. Same applies for the pressure, p, and the nondimensional concentration, C. A dynamic Smagorinsky procedure [Lilly, 1992] implemented following Pierce and Moin [2001, 2004] is used to estimate the eddy viscosity, νSGS, and eddy diffusivity, αSGS, in equations (2) and (3). The corresponding equations are

  • equation image
  • equation image
  • equation image
  • equation image
  • equation image
  • equation image
  • equation image
  • equation image

where ∣S∣ = 2equation image and Sij = equation image. In the previous expressions, Δ is a measure of the local grid spacing and the ratio of the test (equation image) to grid filter width (Δ) is taken equal to 2. The 〈〉 operator refers to local filtering that replaces the usual averaging done in the homogeneous directions in simple flows. The test filter corresponds to an averaging over the neighboring cells. For the present numerical method that is only second-order accurate in space, the commutation error is not accounted for explicitly, as it is of the same order as the discretization error for the terms in the Navier-Stokes equations. The dynamic Smagorinsky model can predict negative values of νSGS and αSGS. Thus, if needed, the values of the subgrid-scale contributions are clipped such that the total viscosity and total diffusivity remain positive within the domain at all times [Zhang et al., 1993]. As seen from (6) and (9) the values of νSGS and αSGS are calculated independently on the basis of the instantaneous resolved velocity and concentration fields.

[22] As the governing equations are integrated up to the wall (Δy1+ ∼ 1, where y+ = yuτ/ν, uτ is the friction velocity and ν is the viscosity) by using a dynamic model in which the model coefficient decays automatically to zero near the walls, the need to use empirical near-wall viscosity corrections (e.g., Van Driest damping functions as is done when employing the classical Smagorinsky model) is avoided. The viscous Schmidt number Sc was taken equal to 1. No assumptions are needed to specify the value of the turbulent Schmidt number as the dynamic procedure predicts directly, on the basis of the resolved velocity and concentration fields, the value of the eddy diffusivity. Locally, the equivalent turbulent Schmidt number in the simulation was found to be up to 100 times larger than the viscous one in the instantaneous flow fields. The code was parallelized using the multiple parallel interface (MPI) library. The simulation discussed in present paper was run on 16 processors of a Xeon PC cluster with Myrinet. Metis was used for domain decomposition.

4. Code Validation

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[23] The code was successfully validated for internal and external flows of various complexities using either laser-Doppler-velocimetry (LDV) or PIV experimental data or results from highly resolved numerical simulations using spectral codes. Specific direct numerical simulation (DNS) and LES validation test cases include isotropic turbulence [Mahesh et al., 2004], turbulent channel flow [Mahesh et al., 2004], massively separated flow around cylinders at several Reynolds numbers [Mahesh et al., 2004], swirling flow in a coaxial geometry [Apte et al., 2003], spatially evolving jets [Babu and Mahesh, 2005] and jets in cross flow [Muppidi and Mahesh, 2005]. Applications in highly complex geometries (jet aircraft engine combustors, realistic geometry water pump intake bays), two-phase flow and reacting flow simulations, including validation results, are discussed by Mahesh et al. [2006], Tokyay and Constantinescu [2006] and Apte et al. [2003]. Validation of simulations involving scalar transport is discussed by Mahesh et al. [2006].

[24] Recently, McCoy et al. [2006b] performed a detailed validation study using the present LES code for the flow in a channel with multiple embayments corresponding to one of the test cases of the scaled model laboratory study of Uijttewaal et al. [2001]. PTV was used in the experiment to collect velocity information at the free surface in several embayments. The Reynolds number was 32,000. Besides the LES simulation, a k-ω RANS simulation was conducted on the same mesh (∼4 million cells) to better put in perspective the predictive capabilities of LES. Streamwise and transverse velocity and normal Reynolds stresses profiles in the free surface plane from experiment and simulation were compared in the first and last embayments. It was found that LES does overall a much better job compared to RANS at capturing the distribution of the mean velocity components and especially of the turbulent kinetic energy across the mixing layer at the channel embayment interface, especially over the downstream half of the embayment length.

5. Simulation Setup

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[25] The computational domain is identical to the one (Figure 1) in the study of McCoy et al. [2006a] with the exception of the channel depth. The height of the groyne, D, is used as the length scale. The total channel depth is h = 1.4 D in the present submerged case (see Figure 2a) compared to 1-D in the emerged case discussed by McCoy et al. [2006a]. The mean velocity in the main channel, U, is used as the velocity scale. The physical domain extends 2-D upstream of the first groyne and 14 D downstream of the second groyne. The Reynolds number defined with D and U is Re = 13,600, identical to the one used in the emerged case. The width of the channel between the two lateral vertical walls is B = 3.75 D. The length, l, and width, b, of each groyne are 0.625 D, and 0.25 D, respectively. The distance between the midplanes of the two groynes is S = 1.5 D such that the embayment length is 1.25 D. In the computational domain, x is the streamwise direction. Its origin is at the inflow section. The centers of the two groynes are situated at x/D = 2.0 and x/D = 3.5.

[26] At the inflow section, the flow fields corresponding to a precalculated fully developed LES open channel simulation conducted at the same channel Reynolds number with periodic conditions in the streamwise direction were fed in a time-accurate way. This ensured the incoming flow was fully turbulent and the turbulent channel flow contained realistic near-wall coherent structures at the location of the upstream groyne. The nondimensional distributions of the mean streamwise velocity, velocity fluctuations in the streamwise and spanwise directions and Reynolds shear stress were found to be in good agreement (see McCoy et al. [2006a] for the emerged case) with the profiles measured in wide channels (top and bottom boundaries were walls in the experiments) at Reynolds numbers (defined with the channel half depth to be consistent with the definition of the Reynolds number in the case of an open channel) in the same range (10,000–20,000).

[27] A convective outflow boundary condition was used at the exit section. This boundary condition allows the coherent structures to leave the computational domain in a physical way and to reduce the distortions associated with the interaction between the structures and the outflow boundary. The velocity boundary conditions on all walls including the lateral wall opposite to the embayment side were no slip.

[28] The free surface was simulated as a rigid lid (open channel) in which the shear stresses in the horizontal directions and the normal velocity were set equal to zero at the free surface. This is generally accepted as a good approximation if the Froude number is relatively low [Alfrink and van Rijn, 1983]. For instance, using the same kind of boundary condition Hinterberger [2004] captured the seiching motions in an array of emerged embayments. The seiching motions were educed by converting the pressure distribution on the free surface into an equivalent water surface elevation using the hypothesis of a hydrostatic pressure distribution close to the free surface. In the present simulation with submerged groynes the Froude number in the channel away from the groynes is close to 0.25 but locally, above the groynes, the Froude number is close to 0.9. The fact that even over the groynes the Froude number remains smaller than one means that the groynes do not act as a local control on the flow (e.g., the flow does not resembles that over a weir, no high-amplitude waves downstream of the groynes are expected, etc.), so in that sense water surface elevation effects are either not important or, more probable, the resulting pressure distribution on the free surface acts in a similar way on the flow away from the free surface as would the presence of a real deformed free surface. Still, nonlinear coupling phenomena between the free surface and the eddies advected beneath it are probably not accounted correctly and results from the present simulation should be interpreted with this limitation of the model in mind.

[29] The mass exchange between the embayment and the main channel was investigated by considering the ejection of a passive scalar that was introduced instantaneously at a certain time (after the velocity fields became statistically steady) inside the embayment domain. The nondimensional scalar concentration C was initialized as C = 1 inside the embayment and C = 0 outside it. The time at which the scalar was introduced was formally taken as t = 0 D/U. The simulation was continued for another 35 D/U until less than 1% of the initial mass of contaminant was left inside the embayment. At the inflow C was set equal to zero. The mass flux was set to zero on all the walls and at the free surface.

[30] The unstructured fine mesh which is used to analyze the flow in the result section contains approximately 4 million hexahedral elements and was generated using a paving technique which allows rapid variation in the characteristic size of the elements while maintaining high overall mesh quality and low stretching ratios. Figure 3 shows the computational mesh in two planes. The views in Figures 3a–3c are situated in a horizontal plane located at the top of the groyne (z/D = 1.0). Figure 3a shows a partial view of the mesh over the whole width of the channel. Figure 3b shows a detailed view around the embayment and Figure 3c shows a detailed view (see rectangle in Figure 3b) of the mesh around the tip of the upstream groyne (the thick lines correspond to the boundaries between the grid partitions corresponding to the processors). Figure 3d shows the mesh in a vertical plane (mid groyne width, y/D = 3.44) over the depth of the channel.

image

Figure 3. Visualization of the mesh. (a) Partial view showing complete channel width in a horizontal plane cutting through the groynes. (b) Detail around embayment region. (c) Detail around groyne tip also showing domain partition on processors. (d) Partial view in a vertical plane.

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[31] The first row of cells from the walls is located within the viscous sublayer (Δy+ < 1). In the vertical direction (82 grid points) the mesh spacing varies from 0.5 wall units at the channel bottom to 22 wall units at the groyne midheight (z/D = 0.5), back to 0.5 wall units at the crest of the groyne (z/D = 1) and then increases to 21 wall units at the free surface, on the basis of the channel Reynolds number and assuming the nondimensional mean friction velocity uτ0/U ∼ 0.05. The mesh size in the regions around (horizontal cell size is close to 50 wall units at point c1 outside the embayment region in Figure 3a) and within the embayment (horizontal cell size is close to 9 wall units at point c2 in Figure 3b) is expected to allow the simulation to capture the dynamically important coherent structures present around the embayment region. The typical dimension of the mesh cells around the tip of the upstream groyne (point c3 in Figure 3c), where the vortex tubes form and are shed in the horizontal detached shear layer (DSL), is close to 3 wall units. The resolution inside the upstream part of the vertical DSL is similar. This is essential to accurately capture these coherent structures that play an important role in the transport of the momentum and mass around the lateral and roof interfaces.

[32] The time step in the simulation was 0.002 D/U. The Courant number inside a typical element within the embayment was 0.06, while outside the embayment region the values were close to 0.04. On the basis of the above elements, the mesh density can be considered fine enough to accurately capture the dynamically important coherent structures in the flow.

[33] To check the grid independence of the fine mesh solution, an additional simulation on a mesh with around 2.4 million cells was performed. Similar to the fine mesh computation, the viscous sublayer was resolved and the first cell off the walls was situated at less than 3 wall units. The mean streamlines, mean velocity and mean vorticity fields were compared in relevant sections. Overall, it was found that the coarse mesh solution agreed well with the fine grid results. Some sample results are reported in Figure 4 for the spanwise profiles of the vertical vorticity magnitude and streamwise velocity at a point situated at z/D = 0.5 (groyne midheight) and x/D = 2.75 (middistance between the two groynes). The profiles are similar and do not show any substantial quantitative differences, including in the region cutting through the horizontal DSL around y/D = 2.75.

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Figure 4. Comparison between fine and coarse mesh solutions on a line parallel to the y direction (z/D = 0.5, x/D = 2.75). (a) Out-of-plane vorticity magnitude. (b) Streamwise velocity.

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6. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

6.1. Analysis of Mean and Instantaneous Vortical Structure of the Flow

[34] Mean velocity streamlines, the distributions of the turbulent kinetic energy (TKE) and various components of the resolved Reynolds stress tensor are used to describe the main vortical structures in the mean flow. Figure 2b locates the planes of interest in relation to the groynes and embayment. The mean velocity fields were averaged over 45 D/U, a time period long enough to ensure convergence of the velocity statistics.

[35] Figure 5 shows 2-D velocity streamlines at four depths in the channel. As expected, for the fairly high relative submergence (1.4) considered in the simulation the flow near the free surface (Figure 5a) is relatively parallel to the mean flow direction. This is consistent with experimental numerical investigations of the flow patterns at the free surface for submerged embayments [Uijttewaal, 2005; Elawady et al., 2000]. Only small deformations are observed in the trajectories followed by the streamlines in the region corresponding to the embayment.

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Figure 5. Visualization of flow structure using 2-D mean velocity streamlines (a) near the free surface (z/D = 1.3), (b) near the groyne top (z/D = 0.9), (c) near middepth (z/D = 0.6), and (d) near the channel bottom (z/D = 0.1). (e) Instantaneous velocity streamlines near middepth (z/D = 0.6).

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[36] The flow in horizontal planes near the channel bed and up to a level situated near middepth of the groyne (Figures 5c and 5d) resembles the flow observed in the fully emerged case [see McCoy et al., 2006a, Figure 4]. A large recirculation region is observed inside the embayment along with secondary corner vortices near the junction between the groynes and the lateral wall (Figure 5c). The shape of horizontal DSL varies with the depth. Near the bottom the area associated with the main recirculation region situated outside the lateral interface is larger. As one goes away from the bottom, the DSL becomes flatter in the region between the two groynes. Because of the presence of the overflow and the associated vertical DSL above the roof interface (z/D = 1) the 2-D streamline patterns near the crest are very different compared to the ones observed in the fully emerged case. The most obvious difference is the fact that the recirculation eddy downstream of the second groyne has practically disappeared at z/D = 0.9 (Figure 5b). In the fully emerged case [see McCoy et al., 2006a, Figure 4], the size of this eddy and the associated reattachment length are increasing strongly as the free surface is approached. At lower levels the eddy is present in the submerged case, but its overall size in the streamwise direction is less than half the value observed in the emerged case. Additionally, in the submerged case a relatively weak vortex is observed upstream of the first groyne especially at midlevels (Figure 5c) near the junction between the groyne and the lateral face. The intensity and size of this vortex appear to be smaller compared to the emerged case [McCoy et al., 2006a, Figures 4 and 5].

[37] Comparison of the mean and instantaneous 2-D streamlines at z/D = 0.6 in Figures 5c and 5e give an indication about the differences between the instantaneous and mean flow. The main difference is the presence of several eddies inside the DSL region in the instantaneous flow fields which are shed from the tip of the upstream groyne and are advected downstream. The Q criterion [e.g., see Dubief and Delcayre, 2000] is used in Figure 6a to educe the 3-D vortex tubes in the instantaneous flow associated with the horizontal DSL (the other vortical structures in the flow were eliminated from the picture). The quantity Q is the second invariant of the (resolved in LES) velocity gradient tensor (Q = −0.5 ∂ui/∂xj · ∂uj/∂xi) and represents the balance between the rotation rate and the strain rate. Positive Q isosurfaces isolate areas where the strength of rotation overcomes the strain, thus making those surfaces eligible as vortex envelopes.

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Figure 6. Visualization of vortex tubes in horizontal DSL. (a) Q criterion and 2-D streamlines (b) z/D = 1.3, (c) z/D = 0.9, (d) z/D = 0.6, (e) z/D = 0.1. Out-of-plane vorticity contours at z/D = 0.5 and (f) t = 0.80 D/U, (g) t = 0.84 D/U, and (h) t = 0.92 D/U.

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[38] These small elongated vortices are a consequence of the growth of the Kelvin-Helmholtz instabilities at the interface between the outer flow and the recirculating embayment flow. Figures 6b–6e show 2-D streamlines in horizontal planes situated at different distances from the bed. Examination of these frames shows that the vortex tubes are relatively irregular, their cores are not exactly vertical and the individual eddies do not extend uniformly from the top of the embayment to the bottom. As they are advected downstream, these tubes are stretched and in some cases they merge with another vortex tube over part of their length to form a stronger vortical structure that in many cases maintains its strong coherence as it approaches the tip of the second groyne. Figures 6f–6h show the vertical vorticity component in a horizontal plane at z/D = 0.6. They illustrate the merging of two vortex tubes a short distance from the formation region close to the tip of the first groyne. This phenomenon is similar to that observed in turbulent mixing layers between two currents of different speed [e.g., see Brown and Roshko, 1974]. Observe that the two vortical structures are distinct in Figure 6g. In Figure 6h the merging of the last two eddies shed in the DSL is complete. Velocity and pressure power spectra show that the range of energetic frequencies (f) associated with the shedding of the vortex tubes from the formation region, expressed in the form of a nondimensional Strouhal number (St = fD/U), is between 3 and 5.5 which is consistent with the frequencies expected to develop in the separated shear layer past bluff bodies at the same equivalent Reynolds number. In the area past the location where the merging of consecutively shed vortex tubes generally occurs, the range of dominant frequencies is between 1.5 and 2.7, consistent with the observed pairing process. The phenomena are qualitatively similar for the vertical DSL.

[39] It appears that in the instantaneous flow visualized in Figures 6b–6e the vortex tubes inside the horizontal DSL (see also instantaneous vorticity contours in Figures 7d and 8d) are advected inside the embayment rather than over the lateral interface area as the mean flow fields would suggest. As discussed later, these coherent structures are responsible for most of the momentum and mass exchange between the embayment and the main channel at both the lateral and roof interfaces. The nature of the interactions with the lateral side and crest of the second groyne (partial clipping, total clipping or total escape events according to the classification by Lin and Rockwell [2001] for cavity flows) controls the intensity of the recirculation motions inside the embayment. The partial clipping event corresponds to partial entrainment of the eddy inside the embayment while the total clipping and total escape events correspond to full entrainment and, respectively, no entrainment (eddy is advected past the embayment). A detailed discussion of the relationship between the occurrence of these events and the pressure fluctuations, vorticity fields and flow patterns inside the cavity/embayment is given by Chang et al. [2006].

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Figure 7. Vorticity and turbulent quantities in a plane situated at midgroyne depth (z/D = 0.5): (a) TKE, (b) equation image/U2, (c) out-of-plane mean vorticity magnitude, and (d) out-of-plane instantaneous vorticity.

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Figure 8. Vorticity and turbulent quantities in a plane situated at midgroyne width (y/D = 3.44): (a) TKE, (b) equation image/U2, (c) out-of-plane mean vorticity magnitude, and (d) out-of-plane instantaneous vorticity.

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[40] As these eddies are not captured in the mean flow, one should be careful when trying to explain the dynamics of a flow dominated by large-scale transport based only on the mean flow fields. In the present paper the instantaneous flow fields are utilized to understand the flow physics pertaining to large-scale unsteadiness and/or intermittency phenomena. For example, the two main vortices upstream of the first groyne and downstream of the second groyne are more deformed in Figure 5e but still recognizable in the instantaneous flow fields suggesting these structures are relatively stable. Analysis of series of instantaneous frames showing the 2-D streamlines demonstrates that these eddies are present at practically all times, though the structure of the downstream recirculation eddy can vary significantly in time.

[41] Figures 7 and 8 show the distribution of the TKE, mean primary shear stress, magnitude of the out-of-plane mean vorticity component and out-of-plane instantaneous vorticity. They serve to educe the similarities and differences between the horizontal and vertical DSLs in the mean and instantaneous flow at equivalent locations. Information provided in Figures 7 and 8 is also of interest for validation of RANS or hybrid RANS/LES models.

[42] The main qualitative difference between the two DSLs is the more curved shape of the horizontal DSL as observed from comparison of the TKE and vorticity contours. The vertical DSL in the mean flow appears to be flatter and fairly parallel to the roof interface because of the presence of the free surface at a relatively low distance over the roof level. This impedes the natural growth of the vertical DSL. The levels of these two quantities are strongly amplified inside the DSLs (by about one order of magnitude in the case of TKE compared to the regions away from the embayment region) mainly because of the advection of the vortex tubes which induces high levels of large-scale fluctuations on top of the background turbulence.

[43] The amplification of the TKE inside the embayment in the region close to the crest of the second groyne in Figure 8a is due to the partial and complete clipping events. As patches of vorticity are injected inside the embayment through the roof interface near the crest of the second groyne, a wall-attached vertical jet like flow forms parallel to the upstream face of the second groyne. This explains the large mean vorticity values observed in that region in Figure 8c. The partial and complete clipping events are modulating the intensity of this jet like flow in time. A similar, though weaker, phenomenon occurs in the horizontal mixing layer where the complete escape events predominate. Evidence of that is given by the visualization of the instantaneous out-of-plane vorticity in Figures 7d and 8d. Three large patches of vorticity associated with vortex tubes are visible inside the horizontal DSL in between the two groynes and a deformed stretched one is observed downstream of the second groyne. The position of the second and third patches strongly suggests (animations confirmed this) that these structures will be advected past the second groyne without interacting with it. The vorticity distribution inside the vertical DSL at the same time instant is different. The last patch of vorticity has just been entrained (total clipping event) inside the cavity while the one behind it will also be totally entrained, or at least interact with the crest of the groyne, such that part of it will be injected inside the embayment (partial clipping). Though examination of animations shows that partial clipping and even total clipping events can happen inside the horizontal DSL, their frequency is much lower compared to that of the total escape events. In contrast, in the vertical DSL the total clipping events dominate. In fact, the mean flow inside the embayment close to the crest of the second groyne shows the presence of a strong downward flow. Such a flow component (spanwise flow toward the lateral wall) is absent in the mean velocity contours at the equivalent position inside the horizontal DSL.

[44] Observe also the wide range of scales and large levels of the instantaneous vorticity associated with some of the eddies present inside the embayment in both planes. They indicate the strong 3-D nature of the flow inside the embayment. However, these medium and small resolved scales are not associated with organized large-scale phenomena, such that the vorticity levels in the mean flow fields are relatively low inside the embayment everywhere except in the attached boundary layers. In Figure 8d several patches of vorticity are advected parallel to the upstream face of the first groyne toward its crest. Once they arrive in the crest region they jitter the vertical DSL. This will induce a strong disturbance into the way the vortex tubes are shed which will last some amount of time. This is one of the mechanisms responsible for the random switching between the different types of interactions among the vortical structures in the DSLs and the extremities of the downstream groyne.

[45] The other region of high amplification of the mean out-of-plane vorticity is situated at the side extremity/crest of the upstream groyne (Figures 7c and 8c) where the vortex tubes are shed at a frequency that is strongly dependent on the physical Reynolds number in the horizontal/vertical DSLs. Though the TKE amplification levels in the embayment region in the two DSLs are similar, the decay downstream of the second groyne is somewhat different. The differences are even clearer when the primary resolved shear stress in the corresponding horizontal and vertical planes are compared in Figures 7b and 8b. Between the two groynes the amplification of the primary shear stress is higher in the horizontal plane. The shear stress values in the horizontal plane are relatively large up to two embayment lengths downstream of the second groyne at the interface between the DSL and the downstream recirculation region (Figure 5c). In contrast, the decay of the shear stress at the downstream part of the vertical DSL is much faster. The main reason for this is the predominance of the total escape events inside the horizontal DSL and of total clipping events in the vertical DSL for the embayment geometry considered in the test case. In the case of total escape events the highly energetic patches of vorticity will continue to be advected downstream of the second groyne. This will induce larger Reynolds stresses in the horizontal DSL past the second groyne. In the case of the vertical DSL, most of these patches of vorticity are injected inside the embayment and relatively few of them will be advected past the second groyne.

[46] To make the analysis easier to follow the above discussion made a distinction between the vertical and horizontal DSLs. In fact, these two DSLs are continuous and one should rather talk about a continuous sheet of vorticity associated with the DSLs originating around the crest and lateral side of the first groyne. Besides the vortex tubes that populate this vorticity sheet a trailing edge vortex forms at the corner of the upstream groyne. Its direction is predominantly streamwise. Figure 9 shows the TKE distribution in a spanwise plane (x/D = 2.75) situated at middistance between the two groynes. The dashed line indicate the relative position of the groyne location relative to the lateral and bottom walls. The shape of the vorticity sheet as well as the small TKE amplification near the corner associated with the trailing vortex can be inferred from this picture. It appears that at midembayment length the intensity of the turbulent fluctuations inside the vertical DSL is larger compared to one in the horizontal DSL.

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Figure 9. TKE contours in plane situated at midembayment length (x/D = 2.75).

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[47] To better understand the mechanisms responsible for the ejection of a passive scalar from the embayment one should first try to visualize the main 3-D eddies in the embayment area. Then, one can try to understand their interaction and ultimately their role in the mass exchange processes between the embayment and the channel. The analysis is quite difficult in the submerged case as the degree of three-dimensionality of the flow is very high, and the instantaneous energetic coherent structures of the flow can be very different compared to the eddies in the mean flow solution. Still, examination of the instantaneous flow fields show that some of the 3-D structures observed in the mean flow have a clear correspondent in the instantaneous flow.

[48] The 3-D and 2-D streamlines in Figure 10 serve to elucidate the flow in the complex recirculation upstream of the first groyne, in particular the interaction between the vertical corner vortex and the junction vortex which forms at the base of the first groyne. The incoming attached boundary layer on the lateral wall separates because of the adverse pressure gradients induced by the presence of the first groyne. Several vortices whose axis is fairly vertical are observed in the instantaneous flow (not shown). The instantaneous vorticity contours in Figure 7d give an idea about the vortical structure in that region at mid groyne height. One of these vortices (see larger patch of positive vorticity in Figure 7d) is larger and relatively stable. The others are generally shed from the separation region and are advected toward the main corner vortex (see Figure 7d). These eddies are created and destroyed randomly. In some cases they can merge with the main corner vortex. In the mean flow only the primary vortex is observed (Figures 5c and 7c). McCoy et al. [2006a] have shown that in the emerged case the main role of this corner vortex was to feed fluid and momentum from the upper layers, starting at the free surface, into the main necklace vortex of the HV system forming at the base of the first groyne. In the submerged case the structure of the system of corner vortices is more complex. As shown in Figure 10a, only the fluid being advected from upstream below z/D ∼ 0.6 is entrained into the corner vortex that feeds fluid into the HV system. This suggests that the dynamics of the corner vortex [e.g., see also Paik et al., 2004] may have an important effect on the dynamics of the HV system and on the scouring process in the case in which the bed is loose.

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Figure 10. Mean velocity streamlines visualizing vortex system in the upstream recirculation region: (a) 3-D streamlines with inset showing vortical structures visualized using Q criterion and 2-D streamlines at (b) z/D = 1.3, (c) z/D = 0.9, (d) z/D = 0.5, and (e) z/D = 0.1.

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[49] Part of the incoming fluid between z/D ∼ 0.6 and z/D ∼ 0.9 is also entrained into a corner vortex. However, the flow inside the core of this corner vortex is toward the free surface rather than toward the bottom as is the case for the corner vortex present at the deeper levels. The core of this corner vortex also changes orientation from being initially vertical to becoming parallel to the lateral wall. In fact, at the junction between the groyne and the lateral wall, close to the crest, a HV system is present. Observe also that in the mean flow a secondary weaker vortex is present (Figures 10a and 10c) close to the lateral wall upstream of the main corner vortex. The Q criterion (inset in Figure 10a) shows only one main continuous structure corresponding to the two corner vortices and the two necklace vortices at their ends, and the secondary vortex at levels close to the free surface. This is somewhat expected if the relative submergence is high, such that in the vicinity of the upstream groyne there is a similarity between the obstructing effect of the groyne relative to the lateral wall and to the bottom given that the incoming flow is parallel to both these surfaces and no stratification effects are considered. This also explains the qualitative similarities observed between the vertical and horizontal DSL over the roof and lateral interfaces. As for the flow over groynes in a loose bed channel it is the HV system present at the base of the first groyne on the bed surface and the accelerating flow around the groyne tip that cause scouring problems, the next section will concentrate on an analysis of its structure. However, an amplification of the shear stress on the lateral wall is also present, near the crest level, around the first groyne for similar reasons.

[50] The mean flow fields are much less helpful in understanding the complex interactions taking place within the embayment volume. However, it appears that most fluid particles inside the embayment will follow a helicoidal path induced by a large 3-D vortical eddy bounded by the vorticity sheet associated with the horizontal and vertical DSLs. This eddy plays a major role in the movement of fluid between different levels within the embayment. As shown by the 3-D streamlines in Figure 11a, its core starts by being perpendicular to the lateral wall and ends being perpendicular to the bottom. The cuts through the embayment volume, parallel to the lateral and bottom walls and situated at small distances from them, confirm the presence of a large vortical motion induced by the overflow and the lateral flow in these sections. The flow inside this mean vortical structure appears to be from the lateral wall and the bottom wall toward the central part of the embayment.

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Figure 11. Mean velocity streamlines visualizing vortices inside the embayment region: (a) 3-D streamlines and 2-D streamlines at (b) z/D = 1.3, (c) z/D = 0.9, (d) z/D = 0.5, and (e) z/D = 0.1. Also shown are (f) diagonal section and (g) y/D = 3.19, (h) y/D = 3.44, and (i) y/D = 3.69.

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[51] The flow downstream of the second groyne is also more complex than the one observed in the emerged case where a main tornado like vortex was observed to originate at the bed and to increase its section as the free surface was approached. In the submerged case such a vortical structure is present as shown by the 3-D streamlines in Figure 12a but it extends only up to levels around 0.6D (e.g., it is present in sections situated at z/D = 0.1 and 0.5 but not at z/D = 0.9 where only a small junction vortex is present, as shown in Figures 12b–12d). The flow direction inside this vortex is away from the bottom. At higher levels, a vortex originating at the lateral wall is observed in Figures 12a and 12e. Its axis is initially perpendicular to the lateral wall. Its center is situated slightly below the crest of the groyne and the fluid particles entrained into this vortex are advected away from the lateral wall. The core of this vortex curves toward the vertical direction as one moves away from the lateral wall. The end effect is that fluid particles entrained into these two recirculation eddies in regions close to the lateral and bottom walls are eventually advected into the mainstream somewhere between z/D = 0.6 and z/D = 0.9. The overall size of the recirculation region associated with these vortices (see also Figures 24a and 24e) is much smaller compared to the one observed in the emerged case.

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Figure 12. Mean velocity streamlines visualizing vortex system in the downstream recirculation region: (a) 3-D streamlines and 2-D streamlines at (b) z/D = 0.9, (c) z/D = 0.5, (d) z/D = 0.1, and (e) y/D = 3.69.

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6.2. Horseshoe Vortex System and Bed Shear Stress Distribution

[52] The structure and overall intensity of the horseshoe vortex (HV) system forming at the base of abutment like structures (in the present case the first groyne) placed in a fully turbulent incoming flow are known to undergo large spatial and temporal variations. As the flow approaches the first groyne, as a result of the transverse pressure gradients and of the downflow, the incoming boundary layer separates and necklace like vortical structures form around the base of the groyne. These vortices are stretched as they are swept around the tip of the groyne. Then they are lifted from the channel bottom and dissipated into the downstream flow. These eddies are though to control, to a great extent, the evolution of the scour process [Dargahi, 1990] which in some cases can endanger the structural integrity of the first groyne. The following groynes are more protected and horseshoe vortices either will not form or will be much weaker compared to the HV system developing at the base of the first groyne in the series.

[53] The mean spatial structure of the HV system is shown in Figures 13a–13c using 2-D streamlines in vertical planes (see also Figure 1a). The first plane makes a 25° angle with the lateral wall, the second one makes a 35° angle and the last one makes a 55° angle. The mean HV system is composed of a primary necklace vortex A and an elongated eddy upstream of it denoted B. Vortex A is initially parallel to the upstream face of the groyne. Then, its core changes orientation and follows the curved shape defined by the horizontal DSL near the bed. Figure 13d (35° section) shows that the TKE is significantly amplified within the region occupied by the main necklace vortex. The turbulence inside the HV system dominates the background turbulence consistent with previous experimental investigations of junction flows [e.g., Dargahi, 1990; Simpson, 2001]. The strong amplification of the pressure fluctuations and TKE (by about one order of magnitude compared to the incoming channel turbulence consistent with the experiments of Devenport and Simpson [1990] for flow past a wing shaped body and with the LES of Kirkil et al. [2006] for the flow past a circular bridge pier) inside the HV system explains, at least partially, the effectiveness of the HV system in removing sediment in the case of a loose bed.

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Figure 13. Structure of mean HV system as it wraps around the upstream groyne base in several vertical planes making an angle with the lateral wall: (a) 2-D streamlines, 25° plane; (b) 2-D streamlines, 35° plane; (c) 2-D streamlines, 55° plane; and (d) TKE, 35° plane.

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[54] The instantaneous 2-D streamlines in Figures 14 and 15 (35° section) allow a better understanding of the vortical structure and flow dynamics within the HV system in a section where its overall intensity is close to the peak. The flow inside the HV system is characterized by random interactions among the necklace eddies. Animations in several vertical planes show that the primary necklace vortex A is practically always present though its shape and size can vary considerably over time.

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Figure 14. Temporal evolution of instantaneous HV system in a vertical plane making a 35° angle with lateral wall: (a) 1.44 D/U, (b) 1.76 D/U, (c) 1.92 D/U, and (d) 2.36 D/U.

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Figure 15. Temporal evolution of instantaneous HV system in a vertical plane making a 35° angle with lateral wall: (a) 0.12 D/U, (b) 0.44 D/U, (c) 0.6 D/U, and (d) 0.76 D/U.

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[55] It is also observed that the primary vortex A in the mean flow corresponds to the instantaneous vortex A in Figures 14 and 15. In contrast to this, no instantaneous vortex can be directly associated with the elongated eddy denoted B in Figure 13. This eddy is a result of averaging process. It is associated with the secondary vortices that are shed from the separation region toward the main necklace vortex A in the instantaneous flow (e.g., C, D, E in Figure 14 or F, G in Figure 15). No definite frequency can be associated with the shedding of these secondary necklace vortices. The range of Strouhal numbers associated with the advection of these eddies toward the main necklace vortex and with their oscillations is between 0.45 and 2.3. Besides these frequencies, velocity and pressure power spectra show the presence of energetic frequencies between St = 0.12 and St = 0.29. These lower frequencies are associated with aperiodic oscillations [e.g., see Devenport and Simpson, 1990; Simpson, 2001] of the primary vortex. It is interesting to notice that the ratio between the mean frequency associated with the aperiodic oscillations and the main frequency associated with the shedding and advection of secondary necklace vortices (St ∼ 0.45) is close to 0.5 which is practically identical to the result of Devenport and Simpson [1990] obtained in a much higher Reynolds number flow. The primary vortex A oscillates between what is generally called a zero-flow mode in which the primary vortex is situated closer to the groyne base and the near-bed jet flow beneath it is weak and separates early, and a back-flow mode in which the near-bed jet flow is stronger and separates at a larger distance from the abutment. In the back-flow mode the main necklace vortex is advected away from the wall and assumes a more elliptical shape. The oscillations of the necklace vortex A between these two modes are the main reason for the high turbulence intensities observed in the HV region in Figure 13d.

[56] The streamlines in Figure 14 illustrate one of the mechanisms that result in a strong modulation in the intensity of the primary vortex A. Comparing Figures 14a and 14b one can see that the secondary vortex C is moving toward the tip of the groyne while, as a result of its interaction with the secondary wall-attached vortex, the primary vortex is moving away from the groyne tip. The two vortices A and C start interacting and eventually merge in Figure 14c. The merging is practically complete in Figure 14d, where the following secondary necklace vortex D starts moving toward the new primary vortex A.

[57] Another mechanism that results into a large variation of the structure and intensity of the primary vortex A is illustrated in the successive frames in Figure 15. In this case the interactions with the secondary vortices advected from the separation region of the incoming boundary layer are negligible. As a result of the change in the intensity of the downflow, the secondary wall-attached vortex, WA, that is present at most times immediately upstream of vortex A growth such that its size and intensity are comparable to that of the primary vortex A (Figure 15b). Concomitantly, this secondary vortex is swept away from the bed and starts merging with the primary vortex as shown in Figure 15c. In Figure 15d the merging is complete and the size of the primary vortex A has grown considerably compared to its mean size.

[58] Figure 16 shows the contours of the nondimensional bed shear stress relative to the mean value (τ0 = ρuτ02 where uτ0/U = 0.052) corresponding to fully turbulent flow in a channel of identical section without groynes. The mean bed shear stress τ/τo distribution in the emerged [McCoy et al., 2006a] and submerged cases are plotted in Figures 16a and 16b. Qualitatively the bed shear stress distributions look similar. The maximum values of τ/τo are close to 15 in the submerged case and to 16 in the emerged case in the strong acceleration region near the tip of the upstream groyne. This is consistent with previous experimental observations [e.g., see Melville and Coleman, 2000] of the scour at bridge abutments (isolated spur dike) that show that scour is initiated in the region around the tip of the groyne. Once the scour hole starts forming, the largest bed shear stress values are recorded beneath the main eddy of the HV system. The large amplification of the bed shear stress around the tip of the upstream groyne indicates that severe scour can occur at the base of the first groyne. By comparison, the amplification around the second groyne is very small.

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Figure 16. Analysis of bed shear stress distribution and near bed turbulence. (a) Mean τ values, emerged case. (b) Mean τ values, submerged case. (c) Instantaneous τ values, submerged case. Submerged case, time series of τ at points (d) p11, (e) p12, and (f) p13. Emerged case, histograms of τ at points (g) p11, (h) p12, and (i) p13. Submerged case, histograms of τ at points (j) p11, (k) p12, and (l) p13. Submerged case (m) pressure RMS fluctuations near the bed, and (n) TKE distribution near the bed.

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[59] For reference, the critical bed shear stress τcr corresponding to entrainment conditions was calculated using Shield's diagram for a sediment size of d50 = 0.45 mm assuming D = 0.08 m and U = 0.171 m/s which is consistent with Reh = 19,000. The critical shear velocity was estimated to be 0.016 m/s (uτcr/uτ0 ∼ 1.8) and the particle Reynolds number was equal to 6.13. This gives a critical bed shear stress for sediment entrainment of τcr = 0.035ρU2. It corresponds to a value of τcr/τo equal to 3.3. This is the reason the values beneath 3.3τ0 were blanked in Figures 16a–16c. Observe that the entrainment area is slightly larger in the emerged case. This may look counterintuitive knowing that generally scour is more intense at flood conditions. However, the present results are consistent with this observation. The two nondimensional distributions in Figures 16a and 16b take automatically into account the additional water depth at flood conditions while the mean incoming velocity is assumed to be identical. However, this is not the case when flooding occurs. Typically the mean velocity in the channel is higher (roughly proportional to the hydraulic radius at power 2/3) and thus same is true for the Reynolds number in the submerged case. Assuming scale effects are relatively small between the Reynolds numbers corresponding to normal and flood conditions (the incoming flow is fully turbulent in both cases), the distribution of the dimensional bed shear stress will show that higher values are predicted and the entrainment region is larger in the submerged case which is associated with real flood conditions.

[60] The instantaneous distribution of τ/τo in Figure 16c shows the large variability of the bed shear stress distribution and the direct correspondence between the intensity of the coherent structures above the bed (e.g., vortex tubes being advected inside the DSL, primary and secondary necklace vortices whose intensity vary along their axes) and the bed shear stress value. Typical variations of the τ values around the mean value are of the order of 1.5τ0 in the region of high bed shear stress amplification beneath the HV system and in the upstream part of the horizontal DSL as also observed from the time series of the nondimensional bed shear stress in Figures 16d–16f. The positions of points p11, p12 and p13 are shown in Figure 16a. In this regard, the coherent structures responsible for most of the sediment transport phenomena around groynes are different than those playing an important role in channels containing ripples or dunes where sweep and ejection phenomena and kolk vortices play the most important role in sediment entrainment, transport and deposition. Locally, around the embayment region, the influence of these structures on local scour phenomena in the case of a loose bed is much smaller compared to that of the energetic eddies associated with the HV system, the horizontal DSL and the recirculating motions within the embayment.

[61] One of the quantities of real interest for sediment transport phenomena is the local probability that the instantaneous bed shear stress is larger than the critical value for sediment entrainment (τcr). This quantity is very relevant for flow around hydraulic structures in which large-scale coherent structures (e.g., necklace vortices in the HV region, vortex tubes in the DSL) are responsible for scour phenomena. To estimate this quantity one has to first compute the histograms of the instantaneous bed shear stress. Figures 16g to 16i show the probability plots (histograms) for the emerged case and Figures 16j–16l display the probability plots for the submerged case at the same points. The value of τcrit is also marked on these plots. As already discussed, if the same channel bulk velocity is present in both the emerged and submerged cases, than the overall intensity of the HV system and the associated bed shear stress levels are expected to be higher in the emerged case. This is clearly seen by comparing the corresponding histograms for the emerged and submerged cases in Figure 16. Observe also that the range of the recorded bed shear stress values around the mean (the variance) is larger in the emerged case. This larger variance is also expected to be present at points where the mean bed shear stress is smaller than the critical value, but where instantaneous values can be larger than the critical value. If a classical RANS model would be used then the model would predict no sediment entrainment to occur at that position. This is obviously wrong, as entrainment of sediment particles can occur at those locations in a more intermittent fashion. Thus, at the minimum variance of the bed shear stress along with the mean bed shear stress, distribution should be used with simpler RANS models to determine whether or not sediment will be entrained locally and then to determine the value of the bed load transport rate. Deterministic (e.g., using a transport equation) or semistochastic models for estimation of the local bed shear stress variance are still to be proposed for complex flows in which massive separation is present. In this regard LES or hybrid LES-RANS models that resolve the variations of the bed shear stress induced by the passage of the resolved large-scale coherent structures can account for these phenomena without need for extra modeling and are more appropriate for applications in which prediction of sediment entrainment from the bed is of interest.

[62] On the basis of the results in Figure 16, in the emerged case the bed shear stress at point 11 (Figure 16g) has a cumulative probability (calculated by integrating the probability up to the threshold value from the histograms shown in Figure 16) of 1.0 for being greater than the critical bed shear stress. At point 12 the cumulative probability is close to 0.90 (Figure 16h) and at point 13 is close to 0.93 (Figure 16i). In the submerged case the cumulative probabilities at points 11, 12 and 13 are equal to 1.0, 0.45 and 0.69, respectively.

[63] Finally, LES allows obtaining information not only related to the TKE variation in the near bed layer (z/D = 0.05) but also the distribution of the pressure RMS fluctuations at the bed. These quantities, that along with the bed shear stress play an important role in the entrainment of sediment in the case of a loose bed, are plotted in Figures 16n and 16m, respectively. Though both quantities are amplified beneath the HV system and the separated shear layer, their distribution is not identical. They also illustrate the observation that for massively separated flow around hydraulic structures it is the large-scale vortical structures induced by the adverse pressure gradients and separation (e.g., the large-scale necklace vortices at the base of the upstream groyne and the vortical structures that populate the DSL) that play the most important role in the scouring process. The high spatial and temporal variation of the bed shear stress distribution around the embayment region suggests that successful numerical prediction of sediment transport and scour phenomena for flow around groynes requires the use of numerical techniques that have the capability to capture the large scales and main macroturbulence events responsible for this variability.

6.3. Mass Exchange Processes Between Channel and Embayment

[64] Details of the contaminant ejection and dispersion are visualized in Figures 1719 which show contours of the instantaneous concentration as the contaminant is leaving the embayment in a horizontal plane situated at groyne middepth (Figure 17), in a vertical plane situated at groyne midwidth (Figure 18) and in a vertical plane situated at groyne midlength (Figure 19). Note that the concentration levels in Figures 17c, 17d, 18c, 18d, 19c, and 19d (maximum contour level is 0.03) are different from the ones used in Figures 17a, 17b, 18a, 18b, 19a, and 19b (maximum contour level is 0.1) such that the structures and concentration distribution can be clearly identified in the embayment region in the later stages of the removal process. Examination of animations showing the evolution of the concentration C shows that most of the contaminant leaves the embayment area by being entrained into the horizontal and vertical DSLs. As low-concentration fluid from the channel is entrained within the embayment over the downstream part of the lateral and roof interfaces (e.g., observe the difference in concentration between the upstream and downstream parts in Figures 17b and 18b), higher-concentration embayment fluid is pushed parallel to the downstream face of the first groyne toward the lateral side or the crest. Once it approaches the upstream part of these DSLs in which patches of vorticity, corresponding primarily to the vortex tubes, are advected, wisps of high-concentration fluid are entrained in between these structures and carried with them further downstream. This process is illustrated in Figure 20 which shows the vortex tubes visualized using instantaneous out-of-plane vorticity contours and the corresponding concentration contours in a vertical plane cutting through the vertical DSL at two time instances. As the wisps of high-concentration fluid are advected, they mix with the surrounding low-concentration channel fluid because of the intense stretching of the coherent structures that populate these DSLs and because of their breaking into small-scale turbulence (the DSL region is characterized by high levels of the TKE). Except for the fact that the relatively small distance between the roof interface and the free surface impedes on the natural development of the vertical DSL, the mass exchange processes at the roof and lateral interfaces are qualitatively similar. The situation will be different in the case of buoyant contaminants or particulate contaminants.

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Figure 17. Instantaneous contours of contaminant concentration at groyne middepth (z/D = 0.5): (a) t = 2.5 D/U, (b) t = 12.5 D/U, (c) t = 22.5 D/U, and (d) t = 33.0 D/U.

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Figure 18. Instantaneous contours of contaminant concentration at groyne midwidth (y/D = 3.44): (a) t = 2.5 D/U, (b) t = 12.5 D/U, (c) t = 22.5 D/U, and (d) t = 33.0 D/U.

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Figure 19. Instantaneous contours of contaminant concentration at embayment midlength (x/D = 2.75): (a) t = 2.5 D/U, (b) t = 12.5 D/U, (c) t = 22.5 D/U, and (d) t = 33.0 D/U.

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Figure 20. (top) Contaminant concentration and (bottom) out-of-plane vorticity contours in a vertical plane (y/D = 3.3) cutting through the vertical DSL near the crest of the upstream groyne: (a) t = 1.08 D/U and (b) t = 1.20 D/U.

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[65] As many of the coherent structures in the DSLs are advected totally or partially over the second groyne, most of the contaminant entrained into the DSLs over the upstream part of the lateral and roof interfaces will be advected past the embayment region rather than being reentrained into the embayment. Part of this higher-concentration fluid is then trapped into the recirculation region downstream of the second groyne as clearly shown by the relatively high concentration observed for t > 12.5 D/U in Figures 17 and 18. Even at t = 33 D/U when practically all the contaminant was ejected from the embayment volume, contaminant is still trapped immediately downstream of the second groyne. In fact, the maximum concentrations within the channel are observed to occur in this region rather than inside the embayment for t > 18 D/U. A considerable amount of the high-concentration fluid trapped into the downstream recirculation region appears to be entrained by the large-scale eddies in the wake past the embayment toward the free surface (e.g., see Figures 18b and 18c) before being advected downstream in the channel. For the relative submergence considered in this simulation, most of the mixing between the pollutant and the channel fluid downstream of the embayment region takes place laterally (see Figures 17b–17d) by the action of the large-scale structures associated especially with the lateral DSL that engulf patches of higher-concentration fluid and then mix it with the higher-speed channel fluid.

[66] The concentration contours in Figure 19 indicate that the mass exchange process is highly nonuniform over the depth. Though the same was true for the emerged case [McCoy et al., 2006a], there is an important difference. In the emerged case it was shown that over practically the whole duration of the ejection process the concentration within the embayment volume was higher in the bottom layer. An important part of the contaminant from this bottom layer was first advected at higher levels within the embayment before leaving the embayment volume. The overall flux of contaminant within the embayment was from the bottom toward the free surface. In the submerged case, as shown in Figures 19b and 19c, the higher-concentration fluid is situated most of the time in the upper layers of the embayment. Past the initial stages of the ejection process, the lower layer contains lower-concentration fluid and, as will be discussed later, the flux of contaminant leaving the embayment through the channel-embayment interface corresponding to the bottom layer is relatively much larger compared to the emerged case.

[67] To characterize the mass exchange between the groyne field and the channel, one-dimensional transport models based on dead zone theory are used. The equation that is generally used to describe the mass exchange [e.g., see Uijttewaal et al., 2001] assumes that the rate of decay of the mean concentration inside the embayment is proportional to the mean concentration difference between the embayment and the channel:

  • equation image

[68] This practically reduces to assuming an exponential decay of the mean concentration (mass of contaminant inside embayment) in time of the form

  • equation image

where T is the characteristic decay time, k is the nondimensional exchange coefficient related to the characteristic decay time T, M is the contaminant mass fraction (or mean concentration) in the embayment, Mr is the contaminant mass fraction in the channel which is assumed to be zero in the emerged and submerged test cases. The index zero corresponds to the values of the variables at t = 0.

[69] Defining k as simply D/(UT) allows a direct comparison of the decay rates in the emerged and submerged cases. The value of k can be estimated directly from the decay rate of the mass of contaminant in time plotted in a log linear scale. This was done in Figure 21 where besides the results for the submerged case the decay of the contaminant concentration for the emerged case [McCoy et al., 2006a] was plotted. The faster decay observed in the submerged case is simply a result of the fact that contaminant can leave the embayment volume not only though the lateral interface (same area in both cases) but also through the roof interface. Interestingly, in both cases a change in the slope of decay is present when the mean concentration inside the embayment becomes less than 35–40% of its initial value. The fact that for both cases the decays over the initial and final phases are practically linear in the log linear plot means that the concentration decay is exponential and is consistent with equation (2). The estimated values of k are 0.29 and 0.18 over the two phases of decay in the submerged case. The corresponding values for the emerged case are 0.1 and 0.05.

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Figure 21. Contaminant mass decay within embayment volume for submerged and emerged cases.

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[70] In the case of groyne fields in which the bottom elevation inside the embayment region is constant and equal to that inside the main channel, the nondimensional exchange coefficient is often defined for fully emerged groynes [Uijttewaal et al., 2001] as ke = l/(UT) = l/Dk where l is the embayment width (= 0.625 D). For submerged groynes the corresponding definition will also depend on the embayment height (= D) and will take into account that contaminant leaves the embayment volume (= SlD) through the lateral and roof interfaces. Its expression is ks = lD/(l + D) · 1/(UT) = l/(l + D)k.

[71] The presence of two regimes of exponential decay was also observed by Engelhardt et al. [2004] in a field study of the mixing processes around irregular river groynes (the changes in bed elevation between the channel and embayment area were gradual) in a reach of the River Elbe for which a one-gyre pattern (one main recirculation eddy inside the embayment) was predominant in the velocity fields. Their results are consistent with the present results. Interestingly, for an embayment in which a two-gyre pattern was predominant, the number of regimes characterized by different values of the exchange coefficient was found to be equal to three.

6.4. Nonuniformity of Mass Exchange Process Over Depth

[72] In the submerged case there is considerable movement of contaminant among different regions within the embayment before it exits the embayment through the lateral or roof interfaces (see Figure 2b). The embayment volume was subdivided into three layers of equal volume (at the start of the ejection process all the layers contain a third of the total mass of contaminant introduced into the embayment) corresponding to the top, middle and bottom layers (see Figure 2b) to study in a more quantitative way the mass fluxes at the interfaces between these layers and the mass decay within these layers. This kind of analysis is practically impossible to conduct using the usual experimental techniques based on measurement of the depth averaged concentration [Uijttewaal et al., 2001; Weitbrecht et al., 2003] used to study mass exchange processes at groyne fields in which only the depth integrated concentration is measured. The temporal variation of the mass of contaminant within each of these layers (MT1, MT2, MT3 for the top, middle and bottom layers), the instantaneous fluxes through the corresponding part of the lateral interface (F2, F4 and F6), the flux through the roof interface (F1), the one between the middle and top layers (F3) and the one between the bottom and middle layer (F5) are represented in Figure 22. The vertical scale is modified in Figure 22 for t > 15 D/U to better observe the variations of these quantities. The mass decay (−MT) is considered positive when the total mass within the layer is decaying in time. The fluxes through the roof and lateral interfaces are positive when contaminant is leaving the embayment. The fluxes F3 and F5 are considered positive when oriented toward the bottom.

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Figure 22. Contaminant mass fluxes within each layer of the embayment: (a) top (t = 0 to t = 15), (b) top (t = 15 to t = 30), (c) bottom (t = 0 to t = 15), (d) bottom (t = 15 to t = 30), (e) middle (t = 0 to t = 15), and (f) middle (t = 15 to t = 30).

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[73] In the top volume layer (Figures 22a and 22b) the overall mass decay, −MT1, is always positive. The flux through the roof interface, F1, is always oriented upward as in average contaminant is leaving the embayment through this surface. Generally the flux through the lateral interface, F2, is toward the main channel, except for some small time intervals (e.g., for 2.7 < tU/D < 3.7). The flux through the bottom surface, F3, is most of the time toward the free surface (F3 < 0), but there are times when this flux is reversed (e.g., for 2.7 < tU/D < 4.8) and the contaminant is moving from the top layer into the middle layer. The flux through the roof interface, F1, is most of the time larger in magnitude than the flux through the lateral interface, F2. This means that at most times more contaminant leaves the embayment through the roof interface compared to the top third of the lateral interface. The magnitude of the flux through the bottom surface, F3, seems to be highly correlated with the magnitude of the flux through the roof, F1 (F1 ∼ −F3). This means that a substantial part of the flux of contaminant through the roof interface is contaminant that has been advected from the middle layer, rather than being linked to a decay of −MT1. In the initial 1D/U the decay is very fast. Most of this decay is due to the engulfment of high-concentration fluid at the top interface by the eddies inside the DSL (−MT1 ∼ F1 while F2 and F3 are small). Between 1 D/U and 2 D/U the mass decay within the top layer is small (the value of k inside the top layer over this time period is only 0.13) as −F3 ∼ F1 + F2.

[74] In the bottom layer (Figures 22c and 22d), the contaminant mass decay, −MT3, is also most of the time positive. Close to 4 D/U, −MT3 is negative mainly because of the incoming flux of contaminant through the top interface of the bottom layer, F5, that is larger than the flux leaving through the lateral interface F6. The flux F6 is oriented toward the channel during the whole duration of the ejection process. The flux F5 changes orientation quite often. However, its predominant direction is toward the free surface (out of the bottom layer). At most times most of the mass decay within the bottom layer is due to contaminant exiting the volume through the lateral interface as F6 is sensibly larger than −F5. Over the first 3.5 D/U the mass decay within the bottom layer is very high (k ∼ 0.56 substantially higher compared to the mean value k = 0.29 for the whole embayment over the same time period). This is due mostly to the high values of F6 coupled with the nonnegligible contribution from F5 whose direction is into the bottom volume.

[75] In the middle volume (Figures 22e and 22f), the contaminant mass decay, −MT2, is almost always positive. The flux through the lateral interface, F4, is oriented most of the time toward the main channel but there are several time periods (e.g., for 3.7 < tU/D < 5.1 20.5 < tU/D < 21.3) where the flux is reversed and contaminant is advected back into the middle layer from the channel. The variations of F3 and F5 were already discussed. Of the three fluxes contributing to the overall mass balance within the middle layer, the flux through the top surface, F3, has the largest magnitude and is oriented most of the time toward the free surface. The other two fluxes have much smaller magnitudes and at most times tend to cancel out as when one is oriented into the middle layer volume the other is oriented out of it. Thus the main cause of the decay of −MT2 is the contaminant lost through the top surface. Over the first 3 D/U the mass decay within the bottom layer is high (k ∼ 0.46). This is due to the high values of F3, as the contributions of the other fluxes over this period cancel out (F4 ∼ −F5).

[76] The temporal evolution of the relative amounts of cumulative mass is shown in Figure 23. The cumulative mass is defined as the integral of the flux of contaminant passing through one of the surfaces corresponding to the roof and lateral interfaces normalized by the total amount of contaminant present initially inside the embayment, M0 = 0.78 D3C0. These quantities serve to better understand the overall circulation of contaminant within the embayment and the way it exits the embayment volume. The cumulative mass advected at the end of the contaminant removal process through the roof interface and the top, middle and bottom lateral interfaces is 44%, 15%, 12% and 29%, respectively. Another way to interpret the results in Figure 23 is to look at the relative mass advected through the interfaces of these volumes relative to the initial mass in each of these volumes. At the end of the removal process 173%, 35%, and 91% of the initial mass of contaminant present in the top, middle, and bottom embayment layers has been advected into the main channel, respectively. This shows in a quantitative way the nonuniformity of the contaminant removal process and highlights the role played by the 3-D vertical motions inside the embayment.

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Figure 23. Temporal evolution of cumulative contaminant mass transport into the channel through the corresponding embayment-channel interfaces.

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[77] If the fact that a substantial amount of contaminant leaves the embayment through the top interface (44%) was somewhat expected, it appears that in average the extra contaminant comes from the middle layer. The amount of contaminant leaving the bottom layer through the bottom lateral interface (29%) is very close to the initial mass of contaminant in that layer (33%). This is total contrast to the emerged case when the mass of contaminant exiting the embayment through the bottom was much smaller than the initial mass of contaminant in that layer (the mass of contaminant exiting through the bottom, middle and top lateral interfaces were around 17%, 33% and 50%, respectively). In the submerged case it is the middle lateral interface that is the less effective in removing contaminant from the embayment. The roof interface accounts roughly for the same amount of contaminant leaving the embayment as the sum between the middle and bottom lateral interfaces at all stages of the ejection process as observed by comparing the curves labeled as roof + top and top + middle + bottom in Figure 23. Another interesting observation is that most of the contaminant leaving the embayment through the top and middle lateral interfaces does that during the initial phase (t < 3 D/U) which roughly corresponds to one eddy turnover time associated with the largest eddies inside the embayment. After 3 D/U, relatively very little contaminant leaves the embayment through these interfaces. This is in contrast to the contaminant transport through the roof and bottom lateral interfaces.

[78] The results in Figure 23 allow a comparison of the effectiveness of the horizontal and vertical DSLs to remove contaminant form the embayment. About 57% of the total initial mass of contaminant passed through the lateral interface (0.445 D3C0) and 43% passed through the roof interface (0.336 D3C0). The roof interface has an area of 0.78125 D2 and the lateral interface has an area of 1.25 D2. The mass yield of the roof interface is calculated as 0.430 DC0 and the mass yield of the lateral interface is 0.356 DC0 showing that for the present geometry the vertical DSL is about 20% more effective than the horizontal DSL in removing contaminant from the embayment.

6.5. Comparison of the Depth-Averaged Flow Between the Emerged and Submerged Cases

[79] Depth-averaged quantities are compared in Figure 24 between the emerged and submerged cases to try to better highlight the overall differences between the two cases. Knowledge of the distribution of these quantities is also useful for validation of simpler depth-averaged RANS or LES models that are used to predict flow past groyne-like geometries.

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Figure 24. Streamlines and TKE distributions in depth averaged flow. (a) Streamlines, emerged. (b) TKE, emerged. (c) Streamlines, submerged. (d) TKE, submerged. (e) Streamlines, submerged, depth averaging over embayment depth. (f) TKE, submerged, depth averaging over embayment depth.

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[80] The distribution of the 2-D streamlines and TKE integrated between the bed and the free surface is shown in Figures 24a and 24b for the emerged case, and in Figures 24c and 24d for the submerged case. The same quantities integrated only from the bed (z/D = 0) to the roof interface (z/D = 1) are shown in Figures 24e and 24f for the submerged case to facilitate comparison of the two cases. This is needed because as shown in Figure 24c the large value of the relative submergence depth (1.4) induces a strong overflow that explains why the depth-averaged flow pattern in the embayment region does not contain much information on the recirculation pattern around and in between the submerged groynes. The 2-D streamlines in the depth averaged flow show that only a perturbation of the incoming parallel flow occurs over the groyne region, similar to the case of a channel flow with bottom roughness elements. In contrast to that, the 2-D streamlines obtained by averaging only over the depth of the embayment in the submerged case (Figure 24e) give a good idea about the mean flow pattern and main recirculation motions induced by the groynes over the embayment height and are more appropriate to be compared with the depth-averaged streamlines in the emerged case (Figure 24a).

[81] The size of the main upstream and downstream recirculation eddies is much larger in the emerged case. For instance, the downstream recirculation eddy reattaches on the lateral wall after 2l from the downstream groyne in the submerged case and after approximately 6.5l in the emerged case. The recirculation eddies in the region bordered by the embayment and the horizontal DSL are more complex in the emerged case. The larger size of the downstream recirculation eddy and the larger values of the TKE in the DSL past the embayment in the emerged case are due to the fact that the shape of the horizontal DSL is such that most of the eddies shed inside the DSL are advected past the embayment region, while in the submerged case a larger part of the vortex tubes are either totally or partially entrained inside the embayment. Evidence of that is given by comparison of the TKE distributions where a larger part of the streak of high TKE associated with the DSL is diverted toward the embayment around the tip of the second groyne (Figure 24d) in the submerged case. This phenomenon is practically absent in Figure 24b. Thus the number of coherent structures and the streamwise momentum past the second groyne are larger and consequently the decay of the TKE is slower in the emerged case. Even in the region between the two groynes the TKE levels are around 30–40% larger inside the DSL in the emerged case.

[82] Comparison of the TKE distributions in the submerged case depth averaged over the channel depth (Figure 24d) and over the embayment depth (Figure 24f) gives an indication about the importance of the overflow and vertical DSL. The TKE values inside the horizontal DSL are smaller in Figure 24d. This is expected because the horizontal DSL is absent between the crest of the groynes and the free surface. However, the overall TKE distribution is similar in the two pictures. The only difference is observed over the embayment, in particular over the upstream part of it and over the top of the second groyne where the values are higher in Figure 24d. This is due to the contribution of the vertical DSL. The TKE values are very large over the top of the second groyne because the local water depth is only 0.4 D in that region and the vertical DSL is present over the whole local flow depth.

7. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[83] The dynamics of the coherent structures in the flow past two vertical submerged groynes (one embayment) mounted on one of the lateral walls of a flatbed channel was studied and compared with results from a similar investigation in which the groynes were fully emerged. As expected, it was found that the three-dimensionality of the flow in the groyne region was much stronger and the overall vortical system inside and around the embayment was more complex when compared to the emerged case due to the momentum transport taking place at the roof interface. The driving force behind the flow dynamics around the roof interface is the coherent structures that populate the vertical DSL. Qualitatively the development of the coherent structures, their interaction with the corresponding embayment interface and their role in the mass exchange processes between the channel and embayment were found to be similar for the horizontal and vertical DSLs. However, for the geometry considered in the present paper it was found that the coherent structures inside the vertical DSL had a larger chance to be totally or partially entrained into the embayment close to the second groyne compared to the ones advected inside the horizontal DSL. The relative submergence depth was high enough such that the mean flow at the free surface was close to parallel to the mean flow direction in the channel.

[84] The structure and intensity of the HV system at the base of the upstream groyne and the associated bed shear stress distributions were investigated. Consistent with previous experimental investigations of the HV system forming at the base of abutments or isolated groynes it was found that the turbulence and pressure fluctuations were strongly amplified inside the HV system and that the highest bed shear stress was induced beneath the main necklace vortex and in the strong acceleration region near the tip of the upstream groyne. Large temporal variations of the bed shear stress distribution were observed in the region where the bed shear stress was strongly amplified.

[85] The removal of a passive contaminant introduced instantaneously inside the embayment was studied using an advection-diffusion equation and the temporal variation of the mean concentration inside the embayment was calculated. Similar to the emerged case studied by McCoy et al. [2006a] and to the field study conducted by Engelhardt et al. [2004] for an embayment with a one-gyre recirculation it was found the decay process was exponential but cannot be described by a unique value of the exchange coefficient over the whole duration of the contaminant ejection process. The switch between the initially faster exponential decay and the final slower phase occurred after about 60% of the initial mass of contaminant left the embayment, close to the emerged case result. Compared to the emerged case the contaminant removal process was much faster (by about 3 times) because of the additional roof interface and the action of the vortex tubes advected in the vertical DSL.

[86] The LES simulation allowed a detailed study of the nonuniformity of the mass exchange process over the depth, something that is not possible to quantify experimentally using techniques that estimate only the depth-averaged concentration. The decay of the contaminant mass in the top, middle and bottom layers of the embayment and the mass exchange through the corresponding embayment-channel interfaces were studied in detail. It was found that about 44% of the total initial amount of contaminant is exiting the embayment through the roof interface and less than half of the mass of contaminant initially situated inside the middle layer is exiting the embayment through the corresponding lateral interface. A quantity close to the mass of contaminant situated initially inside the bottom layer was found to exit the embayment through the corresponding lateral interface. This shows that a mean upward contaminant motion is present within the top two thirds of the embayment depth.

[87] The present LES simulations provide strong evidence that the 2-D approach (used in conjunction with LES or RANS) is likely to result in poor predictions of the depth averaged flow especially in the submerged case. Effects related to the nonuniformity of the transverse velocity distribution or on the vertical large-scale advection of contaminant within the embayment cannot be accounted for properly in these models. This is important because the 2-D approach received lots of attention because of the fact that it is computationally much less expensive than full 3-D computations and can be relatively easily coupled with a deformable bed module to study sediment transport and bed morphology changes around river groyne structures which is a major river engineering problem. Related to 3-D RANS simulations the large-scale unsteadiness and three dimensionality of the main coherent structures in the embayment region hints toward the need to perform time-accurate simulations using nonlinear turbulence closures, if this approach is to be chosen.

[88] Though the idealized form of the geometry considered is an obvious limitation of the present study, 3-D LES allowed for the first time a detailed quantitative and qualitative investigation of the changes in the vortical structure and mass exchange mechanisms between an emerged and a relatively highly submerged embayment which, in the absence of 3-D PIV-based techniques for concomitant velocity and concentration measurements within the embayment volume, remains the best tool for studying the physics of these flows and quantifying the mass exchange. Some of the observed phenomena, like the differences between the overall strength of the HV system between the emerged case and the submerged one, are expected to be similar for more realistic groyne field geometries. Though this was beyond the scope of the present work, the LES database can be used to perform a more detailed study of the dispersion past the embayment region and of the occurrence of situations when the environment can be considered at risk because of the passage of the contaminant, given a certain set of environmental constraints.

[89] The present simulation demonstrate that high-resolution, eddy-resolving, full 3-D computations can be used toward elucidating the momentum and mass transfer processes in channels with groynes and, eventually, for improving and optimizing groyne design related to the various requirements (navigation, bank stabilization, increasing biodiversity of flora and fauna, providing shelter for fish, locally modifying the phytoplankton abundance) that groynes are expected to fulfill. The simulation results can also be used to validate simpler 3-D or 2-D depth-averaged models used to predict flow around groyne fields.

Notation
b

groyne width.

C

(grid) filtered nondimensional scalar (contaminant) concentration.

D

groyne height.

d50

median sediment size.

F1

flux through the roof interface.

F2

flux through lateral interface between top layer and main channel.

F3

flux through horizontal interface between top layer and middle layer.

F4

flux through lateral interface between middle layer and main channel.

F5

flux through horizontal interface between middle layer and bottom layer.

F6

flux through lateral interface between bottom layer and main channel.

h

channel depth.

h/D

relative submergence.

k

nondimensional exchange coefficient, equal to D/(UT).

ke

emerged nondimensional exchange coefficient, equal to l/Dk.

ks

submerged nondimensional exchange coefficient, equal to l/(l + D)k.

l

embayment width, groyne length.

M

pollutant mass fraction (or mean concentration) in the embayment.

Mr

pollutant mass fraction in main channel.

MT1

temporal variation of the mass in top layer.

MT2

temporal variation of the mass in middle layer.

MT3

temporal variation of the mass in bottom layer.

Re

Reynolds number, equal to UD/ν.

Reh

Reynolds number, equal to Uh/ν.

Sc

viscous Schmidt number.

S

space between midplanes of the two groynes.

St

Strouhal number, equal to f(D/U).

T

characteristic decay time.

t

simulation time.

U

bulk velocity in main channel.

uτ

friction velocity.

x

coordinate in streamwise direction.

y

coordinate in lateral direction.

y+

distance from wall in wall units, equal to yuτ/ν.

z

coordinate in vertical direction.

ν

viscosity.

τ0

nondimensional bed shear stress, equal to ρuτ02.

τcr

critical bed shear stress.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References

[90] The authors would like to thank the National Center for High Performance Computing (NCHC) in Taiwan, in particular, W. H. Tsai, for providing the computational resources needed to perform some of the simulations as part of the collaboration program between NCHC and IIHR–Hydroscience and Engineering.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Numerical Solver and LES Model
  6. 4. Code Validation
  7. 5. Simulation Setup
  8. 6. Results
  9. 7. Conclusions
  10. Acknowledgments
  11. References
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