Journal of Geophysical Research: Oceans

Formation and entrainment of fluid mud layers in troughs of subtidal dunes in an estuarine turbidity zone

Authors


Corresponding author: M. Becker, MARUM - Center for Marine Environmental Sciences, University of Bremen, Leobener Straße, 28359 Bremen, Germany. (mbecker@marum.de)

Abstract

[1] The formation and entrainment of fluid mud layers in troughs of subtidal dunes were investigated in the Weser Estuary, North Sea, Germany, based on hydroacoustic measurements. Near-bed suspension layers were found to consist of a suspension of large mud flocs of variable concentration, ranging from 25 g/L below the lutocline to 70 g/L at the river bed, whereas the gelling concentration was below 70 g/L. Sites of fluid mud formation coincided with the location of the estuarine turbidity zone during slack water. On average, near-bed density gradients were initially observed in dune troughs 1.2 h before slack water, and all fluid mud layers were entrained 2.3 h after slack water. No shear instabilities occurred until 1.8 h after slack water. While the flow was oriented in the dune direction, rapid entrainment was related to the development of the turbulent flow field behind dunes and is explained to be induced by advection of strong turbulence during accelerating currents. Fluid mud layers in dune troughs were entrained at an earlier point in time after slack water, compared to adjacent layers formed on a comparatively flat bed, where dune crests did not protrude from the lutocline.

1 Introduction

[2] In estuaries, settling of suspended sediment during slack water is controlled by flocculation in the water column, resulting in an increase of settling velocities and, accordingly, an increase of the mass settling flux [Eisma, 1986; Manning and Dyer, 2007]. Settling is substantially hindered where near-bed concentrations increase [Mehta, 1984], accounting for the formation of lutoclines, i.e., distinct vertical gradients of suspended sediment concentration [Kirby and Parker, 1983; Vinzon and Mehta, 2003; Wolanski et al., 1989].

[3] Concentrations below the lutocline range from a few grams per liter in case of low-concentrated mud suspensions to more than 100 g/L. In case of fluid mud, the gelling concentration is reached and flocs form a space-filling network [Winterwerp, 2002]. Fluid mud is found in many estuarine systems worldwide, e.g., the Severn Estuary [Manning et al., 2010], the Seine [Lesourd et al., 2003], or the Jiaojiang Estuary [Guan et al., 2005]. Estuarine fluid mud layers severely affect the navigability of shipping channels, inducing an apparent reduction of the nautical depth [Wurpts, 2005]. Consolidation of fluid mud leads to the formation of stable mud deposits, and enormous engineering efforts are required to maintain the nautical depth in harbor basins and navigation channels [Manning et al., 2010; McAnally et al., 2007]. Furthermore, the deepening of the main estuarine channel may cause major changes of hydrodynamic boundary conditions, inducing upstream accumulation of fine sediments and fluid mud formation, as shown, e.g., by Winterwerp [2011] for the high-concentrated Ems estuary.

[4] Slack-water formation of fluid mud in estuaries occurs in the range of the estuarine turbidity maximum (ETM) [Dyer, 1988; Prandle, 2004]. According to the tide-driven displacement of the ETM, fluid mud is formed not only in the center but also upstream and downstream of the tidally averaged location of the ETM. These regions of the estuarine channel are characterized by coarser bed sediments and subaqueous dunes, and fluid mud layers are found in dune troughs, as shown for the Weser Estuary by Schrottke et al. [2006].

[5] In general, entrainment by tidal currents limits the consolidation of freshly formed fluid mud and is, as such, an essential process to understand mud deposition in estuaries. Controlled by the density gradient at the lutocline and the available turbulent energy [Toorman et al., 2002], entrainment of fluid mud in dune troughs is of particular interest, as fluid mud layers are exposed to the dune-specific turbulent flow field.

[6] Fluid mud layers in dune troughs were rarely investigated. Carling et al. [2006] and Fenies et al. [1999] observed ponds of fluid mud retained in troughs of intertidal dunes in the Severn and the Gironde Estuary. Sato et al. [2011] conducted flume studies on the dynamics of fluid mud in troughs of current ripples. With respect to suspended sediment transport over bed forms, investigations focused on the dispersion of noncohesive sediments [Kostaschuk, 2000; McLean et al., 2007; Venditti and Bennett, 2000] or on turbulence modulation in cohesive sediment suspensions over current ripples [Baas et al., 2011].

[7] In this study we describe slack-water formation and subsequent entrainment of fluid mud layers in dune troughs, based on hydroacoustic measurements collected in the Weser Estuary. The term “fluid mud” is used only when the gelling concentration is reached in some part of the suspension layer. The term SSC solely refers to the suspended sediment concentration in the water column above the lutocline.

2 Study Area

[8] The Weser Estuary is located between the Jade Bay and the Elbe Estuary at the German North Sea coast (Figure 1). The tides are semidiurnal with a mean tidal range of 3.5 m at Bremerhaven, varying by about 1 m between spring and neap tides. The hydrodynamic regime is ebb dominated with mean depth-averaged current velocities of 1.3 m/s. The mean annual freshwater discharge amounts to 327 m3/s [Deutsches Gewässerkundliches Jahrbuch, 2005]. The water column is well mixed; slight stratification occurs during flood, neap tides, and times of high river discharge [Grabemann and Krause, 1989; Malcherek, 1995].

Figure 1.

(a) Location of the Weser Estuary at the German North Sea coast. (b) Location of the study area within the Weser Estuary. The ETM is shown at its tidally averaged location during conditions of long-term mean freshwater discharge [Grabemann and Krause, 2001]. Longitudinal surveys were conducted between river km 49 and km 61, covering fields of subaqueous dunes. Stationary measurements were located at river km 62.

[9] SSCs in the ETM of the Weser Estuary vary between 0.1 g/L and 2 g/L [Lüneburg et al., 1975]. Wellershaus [1981] found suspension layers formed during slack water at the river bed with concentrations up to 70 g/L. The ETM covers a river stretch of 15 km to 20 km with a tide-driven displacement of approximately 15 km. Its specific location between Brake (km 41) and Bremerhaven (km 68) depends on river discharge and coincides with the low-salinity reach [Grabemann and Krause, 2001]. Accumulation of mud occurs south of Bremerhaven in the center of the ETM and in deeper parts of the navigation channel along the extent of the ETM [Riethmüller et al., 1988; Schrottke et al., 2006].

[10] The navigation depth below chart datum is 9 m upstream and 14 m downstream of Bremerhaven. The morphology and distribution of surface sediments are highly variable [Schrottke et al., 2006]. Ebb-directed dunes are located upstream of km 55 and form on sandy beds, consisting of fine to medium sand [Nasner, 1974]. The average dune height is 2.5 m, and the average dune length is 50 m. Downstream of km 55, the bed is mainly flat with surface sediments alternating between clay drapes and sandy areas. A field of flood-directed dunes is located downstream of km 58 along the western channel margin [Schrottke et al., 2006].

3 Methods

3.1 Surveys and Instruments

[11] Time series of hydroacoustic data were collected on longitudinal transects in the navigation channel in the Weser Estuary from R/V Senckenberg (Table 1). Transects were collected at both sides of the river with an average distance across the channel between 130 m and 180 m. The study area covered the stretch between river km 49 and km 61 (Figure 1). Current velocities were recorded by means of a down-looking 1.2 MHz acoustic Doppler current profiler (ADCP) (Workhorse, Teledyne RDI) with a cell size configuration of 0.25 m and ping rates varying between 2.4 s and 3.8 s. ADCP data were collected in mode 1 without internal averaging. According to deployment depth and blanking distance, the first measuring point was located 1.8 m below the surface.

Table 1. Survey Overviewa
SurveyDateRiver kmSlack WaterDischargeLunar Phase
  1. aFreshwater discharge data were provided by the Federal Institute of Hydrology (Koblenz, Germany).
I-A15 Jun 200450–54flood212 m3/sspring −3d
I-B16 Jun 200449–53flood spring −2d
II-A07 Dec 200459–61ebb298 m3/sneap +1d
II-B09 Dec 200450–53flood neap +3d
III-A07 Apr 200548–54flood347 m3/sspring −2d
III-B12 Apr 200550–56flood spring +2d
IV-A05 Jul 200549–54flood145 m3/sspring −2d
IV-B06 Jul 200549–53flood spring −1d
IV-C07 Jul 200549–53flood spring

[12] A parametric sediment echo sounder (SES-2000® Standard, Innomar Technology; hereafter referred to as SES) was deployed to detect density gradients in the water column with a high vertical resolution (~0.06 m). The SES operates on a primary frequency of 100 kHz. A secondary frequency of 12 kHz was selected for all surveys. Profiles were generated from SES raw data with the acquisition and postprocessing software as distributed by Innomar. A detailed description of the SES is presented by Schrottke et al. [2006].

[13] The water column close to the river bed was sampled using a Rumohr-type gravity corer [Meischner and Rumohr, 1974], equipped with transparent Perspex core barrels of 2 m length. The cores were quickly recovered, and samples were extracted in down core steps of 0.1 m immediately after recovery. To determine sediment concentration, each sample was filtered and the filters dried and weighed.

3.2 Vertical Density Gradients and River Bed Characteristics

[14] Lutoclines were detected by the sediment echo sounder [Hamilton et al., 1998; Shi et al., 1997]. Schrottke et al. [2006] correlated a relatively strong acoustic reflector in SES profiles with an increase of concentration from 0.3 g/L to 27 g/L, measured at slack water between two adjacent sampling positions along the core barrel. Focusing on suspension layers in dune troughs, detected lutoclines were only considered for the analysis if the reflector characteristics could be clearly described, which required a minimum layer thickness of 0.3 m due to the resolution of SES profiles. Furthermore, lutoclines were only taken into account, if at least three ADCP ensembles were collected along their downstream length, to calculate hydrodynamic parameters with sufficient accuracy (see also section 5).

[15] The vertical position of current velocity measurements with respect to the river bed was determined using the ADCP bottom track range. Taking into account that dune crests were oriented predominantly perpendicular to the main channel, bottom track ranges of transverse-directed beams were averaged (beam 1, port side, and beam 2, bow side). The resulting range was found to correspond well with the uppermost sediment surface in SES profiles. In the presence of near-bed suspensions, the bottom track range either indicated the level of the lutocline or was invalid and manually corrected with respect to corresponding SES profiles (Figure 2a).

Figure 2.

(a) Configuration of measurements in dune troughs. ADCP and SES profiles are shown in the upper and lower panels, respectively. The bed is outlined in the ADCP profile as detected by the bottom track signal. The dashed part of this line indicates the lutocline as detected by the SES. (b) Scheme of the stratified shear layer, developing under hydrodynamic forcing. The suspension layer below is entrapped between leeside and stoss side in the dune trough. Overlined symbols indicate spatially averaged parameters. Vertical profiles of concentration and velocity are marked by inline image, and inline image, respectively. Subscripts indicate meters above the lutocline. Δb is the buoyancy difference.

[16] The leeside angle of asymmetric dunes was measured with respect to the slope of the steepest part of the leeside. Subsequently, the terms “leeside” and “stoss side” are used in a geometrical sense with respect to the main dune direction, also if the tidal flow is oppositely oriented.

3.3 Shear Stress, Stability, and Entrainment

[17] Hydrodynamic parameters used in the analysis were based on ADCP ensembles located within the extent of the detected lutocline in each dune trough, confined by the dashed vertical lines in Figure 2a. The lutocline marks the highest local vertical density gradient, where a stratified shear layer develops under hydrodynamic forcing.

[18] Hydrodynamic parameters were also determined for dune troughs before the initial observation of lutoclines and after the entrainment of fluid mud layers. These troughs were only considered if lutoclines were observed during the time series of the specific transect. Provided that measurements covered the corresponding parts of the tidal cycle, the last measurement before slack water of the respective dune trough without a lutocline was taken into account, such as the first measurement after slack water without a lutocline.

[19] One vertical current velocity profile was calculated for each dune trough by spatially averaging current velocity measurements collected along the extent of the detected lutocline, according to Smith and McLean [1977]. Therefore, current velocity components in Earth coordinates were linearly interpolated in steps of 0.05 m, starting at a height of one ADCP depth cell (0.25 m) above the lutocline, and averaged along lines of constant height above the lutocline. If no lutocline was observed, the river bed was used as the lower boundary. The velocity magnitude was then calculated from interpolated and spatially averaged velocity components. Shear stress was assumed to be invariant of height close to the boundary and current velocities to be logarithmically distributed. The shear velocity u* was determined by fitting measured current velocities to logarithmic profiles (least squares) and applying the von Kármán-Prandtl equation

display math(1)

where inline image is the current velocity at height z above the river bed and κ is von Kármán's constant (κ = 0.4). The shear stress τ was calculated by τ = ρ u*2, where ρ is the water density.

[20] If the flow is oriented in the dune direction, spatially averaged vertical velocity profiles over dunes have been found to consist of two or more log linear segments [Chriss and Caldwell, 1982; Smith and McLean, 1977]. Then, the first segment above the bed is considered to be influenced by grain roughness only. Spatially averaged velocity profiles from several laboratory experiments with fixed dune-shaped roughness elements indicate the height of the first segment, i.e., the lower boundary of the influence of form drag, at a vertical position comparable to one dune height [McLean et al., 2008]. Here the extent of the first segment, presumably unaffected by form drag, was defined according to the average dune height in the study area and further limited to the lower 20% of the water column, where the log law usually applies under zero-pressure-gradient conditions [Nezu and Nakagawa, 1993]. However, due to the specific position of lutoclines in dune troughs, shear stress and shear velocity may be influenced by local pressure gradients.

[21] As exposed to velocity shear, lutoclines represent stratified shear layers, governed by vertical differences of velocity and buoyancy. The stability of associated density gradients is assessed by the gradient Richardson number Rig, relating the buoyancy difference to the velocity shear (Figure 2b). Shear-induced disturbances are dampened for values of Rig ≥ 0.25 and the density gradient is considered stable [Fernando, 1991; Miles, 1961]. Gradient Richardson numbers were frequently used to analyze the stability of lutoclines [Jiang and Mehta, 2002; Wolanski et al., 1989]. Here taking into account a continuous lutocline between leeside and stoss side, suspension layers are trapped between two adjacent dunes, and the time-averaged velocity below the lutocline is zero. Using the lowest available spatially averaged current velocity at the height h of 0.25 m above the lutocline (inline image), the average gradient Richardson number (inline image) reads

display math(2)

where Δb is the buoyancy difference. The buoyancy difference is calculated by

display math(3)

in which g is the acceleration due to gravity and ρ0 and ρL are the densities above and below the lutocline, respectively, depending on sediment concentrations c0 and cL (Figure 2b). Entrainment rates were calculated according to Kranenburg and Winterwerp [1997], who derived an entrainment function for fluid mud from the vertical balance of turbulent kinetic energy. The entrainment rate ue is expressed in terms of the shear velocity. Neglecting viscous effects (inline image), the entrainment function reads

display math(4)

with the bulk Richardson number

display math(5)

where H is the water depth.

3.4 Suspended Sediment Concentration

[22] ADCP backscatter was calibrated with respect to SSC, using water samples taken during stationary deployments at km 62, Blexen Reede, aside the navigation channel [Gartner, 2004, and many others]. Water samples were collected in the profiling range of the ADCP, but not lower than 1.5 m above the bed, during all parts of the tidal cycle. The water absorption coefficient was determined using the empirical formulation of Ainslie and McColm [1998].

[23] In the present case, if sediment absorption is neglected, SSC values sampled in the lower part of the water column relate to uncorrected (underestimated) acoustic backscatter values. Accordingly, the relationship between backscatter and the logarithm of sampled SSC deviates from the theoretical linear relation. The sediment attenuation coefficient depends on particle size [Urick, 1948]; however, particle size distributions were not measured during the surveys. This problem was dealt with as follows: In general, acoustic absorption due to suspended sediment was corrected by an iterative procedure as described by Thorne et al. [1994] and applied by Holdaway et al. [1999] to single-frequency hydroacoustic data. Without a priori knowledge of the actual sediment absorption, different absorption coefficients were tested, optimizing the correlation of the linear fit between absorption-corrected backscatter and the logarithm of sampled SSC. The derived sediment calibration parameters and the related absorption coefficient were applied to all ADCP backscatter profiles.

[24] Depth-averaged SSCs for each dune trough were determined by averaging corresponding SSC profiles, while data located below 1.5 m above the bed were omitted to avoid the influence of near-bed particle size variations. The effect of this measure is discussed in section 6.3.

4 Observations

[25] Sampling suspension layers in dune troughs, three cores were collected during surveys II-A and II-B (Figures 3, core locations; 5, associated hydrodynamic forcing; and 6). Concentrations above the lutocline ranged from 0.3 g/L to 0.5 g/L. All cores showed a trend of concentrations to increase down-core with maximum values of 27 g/L below the lutocline and 70 g/L at the consolidated bed, measured in core R2. R1 and R2 were taken during slack water. R3 was taken 1.3 h after slack water. As observed in the transparent core barrels of all cores, the upper part of the layer below the lutocline consisted of a suspension of mud flocs, which formed a space-filling network in the lower part of the core near the river bed. The transition from floc suspension to floc network was smooth and a specific boundary was not determined.

Figure 3.

Vertical distribution of sediment concentration below the lutocline with respect to height above the bed. Note that all cores were taken at different locations. Horizontal dashed lines indicate the height of the lutoclines as observed in SES profiles. Photos of the transparent core barrels show the consistency of the mud-water mixture, namely, a suspension of mud flocs below the lutocline and a space-filling network of flocs close to the river bed. The gray scale of the photo below the lutocline was inverted for better visibility; the photo was taken without flash and mud flocs appeared dark, originally.

[26] Near-bed profiles of sediment concentration were potentially altered recovering the cores, which might have induced mixing in the core barrels or increased settling due to the reduction of turbulence. However, the first significant down-core increase of sediment concentration was found to correspond exactly to the height of the lutocline above the river bed, as observed in SES profiles, indicating that near-bed concentration profiles were undisturbed.

[27] In general, lutoclines spatially covered 50% to 75% of the dune length (Figure 4). During the tidal cycle, different appearances of the corresponding acoustic reflector were observed. Horizontal lutoclines were recorded during slack water (Figure 4b1). Internal waves were found only during survey III-A, 1 h after slack water (Figure 4c2). Before and after slack water, lutoclines appeared inclined with a positive slope in the current direction and a maximum vertical offset of 0.4 m (Figures 4a, 4b2, 4b3, and 4e). In ebb-directed dunes, interrupted or perturbed lutoclines were observed after slack water (Figures 4c2 and 4d), and gaps in lutoclines were located close to the stoss side of the adjacent dune.

Figure 4.

Different shapes of lutoclines, observed during the tidal cycle. SES profiles are shown with a vertical range of 5 m and a length of 500 m, directed downstream. The aspect ratio is 1:25. Weak acoustic reflectors are indicated by dashed lines. Time is hours after slack water. Black arrows indicate the tidal current direction. Numbers at dune troughs denote the maximum lutocline distance from the bed. All plots depict ebb-directed dunes, except for Figure 4e, showing flood-directed dunes. Figures 4b1, 4b2, and 4b3 present a time series of consecutive transects collected during survey I-B, such as Figures 4c1 and 4c2, collected during survey III-A. White arrows in Figures 4b2 and 4b3 indicate lutoclines with an upward slope in current direction. White arrows in Figures 4c2, 4d, and 4e indicate gaps and perturbations.

[28] The same characteristics were also observed in troughs of flood-directed dunes (Figure 4e), where inclined and interrupted lutoclines were found in dune troughs 1.5 h after slack water. In the same profile, the dune height decreased further upstream, and a lutocline was located on top of the dune crests. There, by contrast, interruptions or an inclination of the lutocline was not observed. It is noted that this lutocline was not considered for the following analysis. The observation is later referred to in the discussion.

[29] Beside these variations of their shape, the observed lutoclines were further differentiated by the strength of the associated acoustic reflector as a relative measure between consecutive transects. Six different combinations of lutocline shape and reflector strength were identified, hereafter referred to as lutocline state (Figure 5).

Figure 5.

Spatiotemporal distribution of lutoclines in dune troughs. Each plot refers to one survey. Each row of plots presents surveys conducted during 1 week of measurements. Transects are shown with respect to location (river km) and time in hours after slack water (SW). Slack water is indicated by dashed vertical lines and was determined for each survey according to the minimum near-bed current velocity, measured by the ADCP. Transects are only shown for the time frame between the first and last observations of lutoclines. Transects with a negative slope in the graph are directed upstream, recorded on the left (western) side of the navigation channel. Transects with a positive slope are directed downstream, located on the right (eastern) channel side. Numbers in boxes refer to plots in Figure 4, indicating the location of SES profiles.

[30] The emergence and subsequent disappearance of lutoclines were captured only during two surveys (Figure 5, surveys I-B and IV-B). During survey II-A, lutoclines were observed between river km 59 and km 61 in a field of flood-directed dunes after the ebb phase (Figure 5, survey II-A; see also Figure 4e), whereas all other observations of lutoclines were located further upstream between river km 49 and km 54, in a field of ebb-directed dunes after the flood phase. Accordingly, currents were oriented against the dune direction as lutoclines emerged and along the dune direction when lutoclines disappeared.

5 Dynamics of Fluid Mud Layers

[31] This chapter describes formation and entrainment of fluid mud layers in dune troughs, analyzed on the basis of lutocline states, current velocity, depth-averaged SSC, and near-bed concentration profiles obtained from core samples. All parameters are summarized in Table 2.

Table 2. Physical Parameters at the Beginning of Each Stage of Fluid Mud Dynamicsa
Stageinline image(m/s)inline image (m/s)u* (cm/s)τ(N/m)2SSC (g/L)CL (g/L)inline imageRibue (mm/s)Lutocline State
  1. aCL is the concentration below the lutocline; values in brackets are estimated. At the beginning of stages II and III, CL is unknown, and inline image, Rib, and ue are not calculated. CL assigned to stage III was obtained from core R2, taken at slack water.
I0.150.332.50.75~0.31(>5.3)0.257500.64inclined weak
II0.090.21.60.40.28    horizontal weak
III0.050.110.20.2327   horizontal strong
IV0.090.21.60.40.08(27)4.610,1000.11inclined strong
V0.130.322.70.740.14242.232800.33inclined weak
VI0.170.423.51.250.25(24)1.319500.56perturbed
VII0.250.65.42.8~0.28     

[32] The relation of lutocline states to tide-driven variations of SSC and shear stress is shown in Figure 6. Each data point refers to the observation of one dune trough. Thereby, each trough was represented by a limited number of ADCP ensembles (between 3 and 10), corresponding to a short duration of measurements, below the integral time scale of the flow (~10 min in a tide-dominated environment, e.g., Soulsby [1980]). Values representing a single trough are thus expected to be influenced not only by Doppler noise but also by local turbulence. They potentially deviate from the mean value, which could be determined measuring for a longer period of time at the respective location. Therefore, data were filtered by applying a moving average filter with a window size of 0.15 m/s (Figure 6, thick line). The resulting trend line also shows the distribution of lutocline states, which were defined for each position along the line as the mode of the corresponding filter window, i.e., the lutocline state encountered most frequently. The same filter was also applied to current velocities close to the bed (inline image), which were required to calculate inline image, referred to in section 5.2.

Figure 6.

Shear stress, shear velocity, and SSC related to current velocity and time. Time is hours after slack water. Velocity is positive after slack water and was measured 1 m above the boundary, i.e., lutocline or river bed. SSC is depth averaged, with data below 1.5 m above the boundary being omitted. Gaps in the trend line are introduced to better differentiate between lutocline states, emphasized also by vertical lines. Core numbers are placed according to the near-bed current velocity measured at the sampling location.

[33] Measurements are also shown in relation to the time after slack water (Figure 6). At first, one specific slack-water time was determined for each survey (Figure 5). The precise slack-water time varies with tidal wave propagation along the channel, while its shape and celerity are further influenced by along-channel variations of morphology and cross section. Tidal wave propagation also depends on discharge and lunar phase and certainly varied between the surveys. Since data were collected during neap as well as spring tide and during both low and mean discharge conditions (Table 1), an average relation between near-bed velocity and time after slack water was derived, based on the complete data set. The relation yields an average time after slack water for each location along the channel according to the specific near-bed velocity (Figure 6, right side).

[34] Subsequently, the dynamics of fluid mud layers are described on the basis of the averaged data set, referring to the trend line. Formation and entrainment of fluid mud are conceptually shown in Figure 7, where stages I to VI correspond to the observed lutocline states.

Figure 7.

Concept of fluid mud formation during the dominant and entrainment during the subordinate tide. Dune shape and suspension layer thickness correspond to dunes depicted in Figure 4d. All stages refer to the different lutocline states as observed in SES profiles. Values of current velocity (inline image) and SSC correspond to the beginning of each stage. Time is hours after slack water. Stages I, II, and III show the accumulation of suspended sediment and fluid mud formation during slack water. Stage IV is governed by velocity shear. Stage V depicts the transition from the influence of shear to entrainment, which occurs during stage VI. The dune-specific distribution of currents and turbulence in the leeside is sketched in the plot of stage VII, with flow oriented in the dune direction.

5.1 Formation of Fluid Mud

[35] Stage I of the formation of fluid mud was characterized by the development of a relatively weak density gradient (Figure 7, stage I), detected by the SES 1.2 h before slack water during decelerating tidal currents, oriented against the dune direction (Figure 4a).

[36] Near-bed sediment concentrations in the trough regions were not measured during this part of the tidal cycle. The minimum density gradient to be detected by the SES is unknown. The density gradient at the lutocline depends on the overall difference of sediment concentration as well as on the thickness of the shear layer, which is controlled by settling properties of particles and small-scale mixing due to local turbulence [Noh and Fernando, 1991; Winterwerp et al., 2002]. Irrespective of the actual process of sediment accumulation, a lutocline develops due to the effect of hindered settling, provided that local turbulence is sufficiently reduced. At a current velocity (inline image) of 0.33 m/s, according to the average gradient Richardson number (inline image), an initial sediment concentration of 5.3 g/L is required for stable conditions below the lutocline (Table 2). However, this solely indicates that in the presence of lower concentrations, a lutocline does not develop under the given forcing.

[37] Observed lutocline shapes were found to correspond to hydrodynamic conditions. A shift from horizontal to inclined lutoclines and vice versa occurred at a current velocity of 0.2 m/s and a shear stress of 0.4 N/m2, both before and after slack water. This indicates that the inclination during stage I was caused by current shear, acting on the lutocline and forcing the suspension layer up the leeside of the adjacent dune. According to the observed reflector strength and estimated initial concentration of 5.3 g/L, the overall density gradient was comparatively weak. Possibly, under these conditions, the shear layer practically reached down to the bed and the suspension layer was initially turbulent, i.e., flocs were subject to small-scale movements not only at the lutocline but within the entire suspension layer.

[38] Stages II and III were characterized by decreasing current shear, as indicated by observations of horizontal lutoclines. Sediment concentrations increased in the suspension layer, taking into account the estimation of the initial concentration of 5.3 g/L compared to concentrations of 27 g/L and 48 g/L below the lutocline, measured in cores R1 and R2 at slack water. The transition from stage II to stage III was marked by a significant increase of reflector strength, indicating an increase of the density gradient and a decrease of the height of the shear layer. Densification up to the gelling concentration and the corresponding decline of turbulence inevitably lead to the formation of fluid mud, as it was observed in core R1 and core R2, where concentrations reached 70 g/L and flocs formed a space-filling network near the river bed (Figure 7, stage III; see also Figure 3).

[39] SSCs in the water column decreased from 0.31 g/L at the beginning of stage I to 0.08 g/L, measured 0.75 h after slack water at the end of stage III. Assuming spatial homogeneity, settling of particles caused the aforementioned increase of concentration. Adversely, no significant decrease of SSC preceded the initial observation of lutoclines in dune troughs at the beginning of stage I.

5.2 Entrainment of Fluid Mud

[40] Stage IV was marked by an increase of current velocities, oriented in the dune direction, and current shear, according to the observed lutocline inclination (Figure 7, stage IV). This is comparable to stage I, while during stage IV, the observed lutocline strength was considerably higher, indicating a relatively strong and steady density gradient. This is confirmed by a comparison of cores R2 and R3, where concentrations below the lutocline did not change significantly, varying between 27 g/L before stage IV and 24 g/L afterward. inline image decreased from 4.6 to 2.2 during stage IV, suggesting that instabilities were dampened at the lutocline.

[41] Stage V was characterized by increasing shear layer thickness and, accordingly, the reduction of the density gradient (Figure 7, stage V), as indicated by the observed reduction of reflector strength. This is ascribed to a further increase of velocity shear. Comparing stage IV and stage V, a reduction of the overall layer thickness was not observed, which is shown, e.g., by a time series of transects presented in Figure 4. There, lutoclines in Figures 4b1, 4b2, and 4b3, represent stages III to V and the layer thickness was, besides the increasing inclination, quasi-constant. Likewise, inline image decreased from 2.2 to 1.3, pointing to an overall stable density gradient, and, together with the stable layer thickness, indicates that no entrainment occurred.

[42] Using a concentration of 24 g/L, as measured in core R3 early during stage V, inline image is based on current velocities spatially averaged for the extent of lutoclines. Regarding the observed inclination, lutoclines most likely protruded into the region of higher velocity shear and increased turbulence, inducing interfacial mixing and an increase of the shear layer at the stoss side of the adjacent dune. This explains variations of reflector strength, which, already low, decreased further in the current direction along the fluid mud layer.

[43] The stability of fluid mud layers is further shown by a comparison of entrainment rates, determined for the beginning of stage I and the end of stage V. An entrainment rate of 0.64 mm/s was determined for the conditions at the beginning of stage I, based on the initial sediment concentration of 5.3 g/L. Stage I was characterized by accumulation of sediments, and any entrainment induced by the turbulent flow field is compensated by settling. Therefore, entrainment is expected to occur if entrainment rates exceed the value determined for the beginning of stage I. For the conditions at the end of stage V, the entrainment rate was still lower, namely, 0.56 mm/s, and provided that settling velocities of flocs at the lutocline are constant, no entrainment occurred during stage V. Then, according to the stability of fluid mud layers, entrained sediments do not contribute to the observed increase of SSC during stages IV and V.

[44] However, the initial concentration of 5.3 g/L at the beginning of stage I was determined as the minimum concentration required for a lutocline to resist shear instabilities. A potentially higher concentration would lead to a reduction of the calculated entrainment rate at the beginning of stage I. It is noted that the aforementioned stability criterion, based a comparison of entrainment rates, holds for initial concentrations of up to 7.2 g/L below the lutocline at the beginning of stage I.

[45] Stage VI, starting 1.8 h after slack water, was characterized by the entrainment of fluid mud layers and the resuspension of the sediments, since no lutoclines were detected at a later point in time (Figure 7, stage VI). During stage VI, lutoclines were strongly affected by interfacial instabilities, as indicated by perturbations observed not only at the adjacent stoss side but along the entire lutocline. The density gradient was significantly reduced. Gaps in the acoustic reflector indicate that the local density gradient was too low to be detected by the SES. By contrast, inline image was 1.3 at the beginning of stage VI, which means that the local production of turbulence due to shear instabilities alone was insufficient to induce the observed entrainment.

[46] Stage VI covered a time frame of 0.5 h. Depending on layer thickness and the individual shape of dunes, fluid mud layers are considered to be rapidly entrained at different points in time during stage VI, which is confirmed by the fact that as already mentioned, a gradual reduction of layer thickness was not observed in the time series. Remarkably, a continuous increase of SSC was measured in the water column during stages IV and V, reaching 0.28 g/L at the beginning of stage VI. No significant increase of SSC was measured during stage VI, as fluid mud layers were entrained.

6 Discussion

6.1 Lutocline Stability

[47] Regarding the formation of a lutocline due to the effect of hindered settling, Winterwerp [2002] expressed the settling velocity in terms of the gelling concentration and showed that settling velocities decrease for concentrations exceeding 3 g/L for a range of gelling concentrations between 40 g/L and 120 g/L. In the core barrels, mud flocs were observed to form a space-filling network close to the bed, indicating that the gelling concentration was below 70 g/L and that the threshold concentration of the hindered settling regime applies to cohesive sediments of the Weser Estuary. This confirms the estimation of the initial minimum concentration of 5.3 g/L at the beginning of stage I, in the sense that settling velocities were reduced, promoting the formation of a lutocline.

[48] The initial minimum concentration was derived from the assumption of lutocline stability parameterized by the local gradient Richardson number. Concerning the transition from unstable to stable conditions, the validity of Rig ≥ 0.25 for a stable density gradient must be questioned, as local production of turbulence due to shear instabilities was found to occur up to Rig ~ 1 [Balsley et al., 2008; Stull, 1993]. Thus, by the time that the lutocline was detected, Rig might have been higher than 0.25. Also, since turbulence is not only locally produced but also advected, the concentration at the beginning of stage I was probably higher than 5.3 g/L, to resist the entrainment potential of the turbulent flow.

[49] At the end of stage V, the adverse pressure gradient in the leeside of the dune crest has so far been neglected. At this point in time during the tidal cycle, dunes were filled partly by fluid mud and a negative step between 0.5 m and 1 m was present. Taking into account the specific position of vertical velocity profiles behind the dune crest, namely, the region between 0.25 m and 1.5 m above the lutocline, local pressure gradients probably had a significant influence on vertical velocity profiles at higher current velocities. In case of local deceleration of flow behind the crest, the logarithmic velocity profile is shaped convex upward, and shear velocity and entrainment rates are considerably overestimated [Dyer, 1986]. This, in turn, indicates that the actual entrainment rate at the end of stage V was smaller than 0.56 mm/s, which, compared to stage I, confirms that indeed no entrainment occurred during stage V.

[50] Any influence of suspended sediment stratification has also been neglected, potentially leading to an overestimation of the calculated shear velocities [Dyer, 1986]. To ignore stratification may be justified as similar SSCs were measured in the water column at the beginning of stage I and the end of stage V (~0.3 g/L), causing equivalent bias in both situations. Admittedly, SSC was determined omitting the lowest 1.5 m above the boundary and the influence of suspended sediment stratification in this region is unknown.

[51] The lack of entrainment during stages IV and V was further shown by the constant layer thickness. According to Kranenburg and Winterwerp [1997] and Bruens et al. [2002], the layer thickness is reduced during entrainment if the ambient flow is more turbulent than the stationary layer below, where concentrations are then constant. This is also seen in results from flume experiments, presented by Sato et al. [2011], who physically modeled the formation of mud drapes in current ripples. During the entrainment phase, the thickness of a layer of fluid mud, formed in ripple troughs, gradually decreased during entrainment. Conclusively, no entrainment occurred during stage IV and stage V.

6.2 Turbulence and Entrainment

[52] As reviewed by Best [2005], the turbulent flow field in the leeside of dunes is governed by the adverse pressure gradient, inducing flow separation, recirculation, and the development of a shear layer. Flow separation depends on the leeside angle. Best and Kostaschuk [2002] found intermittent flow separation for leeside angles up to 14°, suggesting permanent flow separation at higher angles. Paarlberg et al. [2009] used 10° as the critical minimum leeside angle for flow separation in their dune evolution model [see also Wilbers, 2004]. Both thresholds are exceeded by the measured leeside angle of 18° in the study area, and the above-mentioned characteristics of dune-related turbulence are expected to control the flow after flood slack water, when ebb currents are oriented in the dune direction.

[53] However, the observed crests shapes in the study area were highly variable, showing sharp and round crests, as well as partly dredged dunes (Figure 4). Round crests indicate remolding by the subordinate tidal currents, i.e., the flood currents in case of ebb-directed dunes (Figure 7, note the change in crest shapes between stage V and stage VII). In this case, the development of recirculation can only develop after the steep frontal shape of the dune is restored. This may take some time, depending on current velocities and the amount of sand needed to recover the dune shape [Martinius and Van den Berg, 2011]. Conclusively, it is unknown when flow separation starts during accelerating tidal currents and, also, to which degree this is influenced by the concentration gradient in the dune trough.

[54] The position of the shear layer, extending from the crest to the stoss side of the adjacent dune, is not constant but subject to low-frequency vertical “flapping” motions, induced by large-scale turbulent structures, which are generated at the dune crest and advected downstream [Nelson et al., 1993; Simpson, 1989]. This periodic vertical displacement of the shear layer is regarded as one possible mechanism to transport high turbulent kinetic energy toward the lutocline (Figure 7, stage VII). Independent of the actual process of advection of turbulence, either advection along the separation stream line or advection due to wake flapping, we hypothesize that once large-scale turbulent structures are generated at the dune crest, fluid mud layers are rapidly entrained during accelerating currents. This is further supported by observations of Sato et al. [2011]. In their flume experiments, the onset of entrainment of fluid mud in troughs was found to be related to the generation of vortices, shed from the ripple crests.

[55] At the beginning of the entrainment phase, the density gradient was shown to be stable with respect to shear instabilities (inline image), and it was suggested that turbulence generated at the dune crest is responsible for the observed entrainment. This is substantiated by observations of lutoclines, not showing indicators for entrainment in the absence of dune crests (Figure 4e). This indicates that fluid mud layers in dune troughs are entrained at an earlier point in time during accelerating currents, compared to the adjacent layers formed on a comparatively flat bed, where dune crests or other roughness elements do not protrude from the lutocline, and strong turbulent stresses are missing.

[56] The entrainment mechanism was analyzed for the dominant tide, with the tidal flow oriented in the dune direction. Lefebvre et al. [2011] measured vertical current velocity profiles over large dunes in a tidal inlet channel during a tidal cycle. Dune roughness was found to be significantly reduced during the subordinate tide, which may be related to lower levels of turbulence behind the crest. It can only be hypothesized that entrainment of fluid mud layers during the subordinate tide occurs at higher current velocities, compared to the dominant tide. However, such fluid mud layers were not observed during the surveys.

6.3 Suspended Sediment Dynamics

[57] It was shown that no entrainment occurred until the end of stage V, in turn indicating that concentrations below the lutocline were constant during stages IV and V, whereas an increase of SSC was observed in the water column above the lutocline. This may be related to the dispersion of suspended sediment, located within the vertical range of 1.5 m above the lutocline or the river bed, which was omitted calculating depth-averaged SSC. Due to lateral dispersion, other sources aside from the main channel may play a role, such as adjacent muddy areas located closer to the river banks.

[58] SSC measurements conducted in the ETM, presented by Riethmüller et al. [1988] and Grabemann and Krause [2001], show that depth-averaged values between 0.8 g/L and 0.3 g/L are characteristic not for the center but for the upstream and downstream ends of the ETM, which is, with respect to the position of the ETM, in accordance with the observed position of fluid mud layers (see Figure 1 and Figure 6).

[59] This inhomogeneity of SSC in the ETM, together with effects of advection, may further account for the measured SSCs before stage I and during stage VI, where no significant decrease of SSC preceded the accumulation and no increase of SSC followed the entrainment of fluid mud. Most of the fluid mud layers were observed after the flood phase between river km 49 and km 54. While the ETM is shifted upstream during flood, the decrease of SSC due to settling before stage I was potentially compensated by advection of higher concentrated estuarine waters. The opposite effect may have occurred after slack water during stage VI, when fluid mud was entrained and the increase of SSC due to resuspension of sediments was compensated by downstream advection of lower concentrated riverine waters.

[60] Upstream of river km 54, no fluid mud layers were observed in dune fields during and after ebb slack water, which is also ascribed to the tide-driven displacement of the ETM, namely, the downstream shift during the ebb phase and the occurrence of relatively low SSCs upstream of km 54. This supports the general assumption that fluid mud formation, depending on sufficient supply of suspended cohesive sediments, is linked to the slack-water position of the ETM.

6.4 Grain Size Distribution in Dune Troughs

[61] Fluid mud formed during stage III and remained undisturbed for at least 2 h during stage IV and stage V, while turbulence was considered to be dampened at the lutocline. The onset of entrainment at the beginning of stage VI thus confined the time period of consolidation. Concerning self-weight consolidation of flocculated mud, Been and Sills [1981] conducted a settling column experiment under conditions comparable to those of fluid mud in dune troughs. Starting with a concentration of approximately 100 g/L and a height of 1.75 m, after 2 h, a layer of 0.1 m in thickness formed at the bed with a concentration exceeding 280 g/L. Accordingly, the formation of a thin, higher concentrated mud layer at the river bed is considered to be highly probable. This layer may be sufficiently resistant to erosion to survive the initial part of the entrainment phase and mixed or even covered by sand as a result of bed load transport and leeside deposition.

[62] Concerning the lower part of the leeside, Kleinhans [2004] discussed the enrichment by fine sediment due to slack-water deposition, depending on SSC in the water column. Our results indicate that in case of estuarine dunes, fluid mud should be taken into account as a potential source of fine sediments in dune troughs. The suggested mud deposition and associated change of grain composition would also increase the local erosion threshold of sandy trough sediments [Torfs et al., 2000].

7 Conclusions

[63] The formation and entrainment of ephemeral fluid mud layers in the troughs of subtidal dunes were analyzed on the basis of hydroacoustic measurements, collected in the range of the ETM of the Weser Estuary. Fluid mud layers were formed after the subordinate tide, and entrainment occurred during the dominant tide. Different stages of the development of fluid mud were related to environmental parameters, derived from a comprehensive data set, which covered various hydrodynamic conditions with respect to discharge and tidal phase. The gained understanding is regarded to be applicable not only to the Weser Estuary but, in general, to fluid mud dynamics in troughs of large dunes in estuaries with a pronounced ETM.

[64] From the results of this study, the following conclusions are drawn:

  1. [65] In the Weser Estuary, near-bed suspension layers in dune troughs consist of a suspension of large mud flocs of variable concentration, ranging from 25 g/L below the lutocline to 70 g/L at the river bed, where the gelling concentration is reached and mud flocs form a space-filling network.

  2. [66] Regarding the extent of dune fields considered in this study, sites of fluid mud formation correlate with the location of the Weser ETM during slack water.

  3. [67] From the initial observation before slack water to entrainment after slack water, the overall maximum residence time of suspension layers in dune troughs is 3.5 h in the Weser Estuary. From the first observation of fluid mud, the time frame of consolidation is 2 h, limited by the onset of entrainment.

  4. [68] No shear instabilities occur prior to entrainment, until 1.8 h after slack water. However, during this period, the fluid mud layer is subject to hydrodynamic forcing, inducing an inclination of the lutocline in the current direction under the influence of current shear.

  5. [69] Rapid entrainment is related to the development of the dune-specific turbulent flow field behind the dune crest during accelerating currents, oriented in the dune direction. The entrainment is not induced by the breakdown of shear instabilities but by strong turbulent stresses, produced at the dune crest and advected in the direction of the lutocline.

  6. [70] During the dominant tide, fluid mud layers in dune troughs are entrained at an earlier point in time during accelerating currents, compared to adjacent layers formed on a comparatively flat bed, where dune crests or other roughness elements do not protrude from the lutocline and where strong turbulent stresses are missing.

Notation
Δb

buoyancy difference.

CL

sediment concentration below the lutocline.

H

water depth.

κ

von Kármán's constant.

inline image

average gradient Richardson number.

Rib

bulk Richardson number.

ρ

water density.

ρ0

water density above the lutocline.

ρL

water density below the lutocline.

τ

bed shear stress.

inline image

current velocity, spatially averaged.

inline image

current velocity, spatially averaged, 0.25 m above the boundary.

inline image

current velocity, spatially averaged, 1 m above the boundary.

u*

shear velocity.

ue

entrainment rate.

z

height above the boundary.

Acknowledgments

[71] This study was funded through DFG-Research Center/Excellence Cluster “The Ocean in the Earth System.” The Senckenberg Institute is thanked for providing the ship time. The authors thank the Innomar Technology GmbH, Germany, for the kind provision of the SES-2000®. The Federal Institute of Hydrology, Koblenz, Germany, is thanked for providing river discharge data. Also appreciated is the assistance of the captain and crew of the R/V Senckenberg, who did an excellent job during the cruises. Finally, the manuscript improved substantially from comments and suggestions by Janrik van den Berg and two anonymous reviewers, the Associate Editor, and the Editor, who are all thanked for their engaged reviews.

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