Journal of Geophysical Research: Earth Surface

Micro-topographic analysis of shell pavements formed by aeolian transport in a wind tunnel simulation

Authors


Corresponding author: C. McKenna Neuman, Department of Geography, Trent University, Peterborough, ON K9J 7B8, Canada. (cmckneuman@trentu.ca)

Abstract

[1] Beach surfaces containing shell materials represent one end-member of a range of environments in which armoring is the primary control on wind erosion. Unlike spheres and cylinders which have formed the basis of theoretical model formulation and much of the early work in wind tunnels, mollusc shells have complex and non-uniform shapes which vary with their orientation. Identification of shell perimeter, height and frontal area relative to the bed area (roughness density) is therefore a formidable task, but nonetheless is essential for modeling sediment entrainment from beach surfaces. A methodology is suggested in this paper for capturing and analyzing these geospatial data, in the context of a wind tunnel simulation designed to improve understanding of the geophysical processes involved in armoring. For deposits where non-erodible shells represent half of the volume of the parent material, the surface appears to be highly stable to wind erosion from the outset, although minor reworking of the intervening, erodible sediment does occur. In comparison, the shell coverage must increase to approximately 30% during wind erosion events in order for any given beach surface to stabilize, especially beach deposits with a low concentration of shells by volume. With suitable calibration, the Raupach shear stress partitioning model can be forced to perform well in predicting the threshold conditions for particle entrainment. However, this approach overlooks the pivotal involvement of particle impact and ricochet in the creation and sculpting of the armored bed. As a case in point, when the shells are removed from digital elevation models of armored beach surfaces formed in aeolian systems, the adjusted topography is not suggestive of the presence of coherent flow structures (e.g., horseshoe vortices and wedge shaped shelter areas) as assumed to exist in the stress partitioning approach for isolated flows. This would suggest that future work on the armoring of natural surfaces affected by wind erosion must allow for more complexity in the flow perturbation.

1. Introduction

[2] Armoring as a geophysical process plays a crucial role in reducing erosion. It is recognized to operate in a wide range of environments, inclusive of dryland (aeolian) [e.g., Nickling and McKenna Neuman, 2009], coastal [e.g., Davidson-Arnott et al., 1997] and fluvial systems [e.g., Parker et al., 2007]. However, air is three orders of magnitude less dense than water and one hundred times less viscous. Threshold velocities for the entrainment of particles of equivalent size are considerably greater for atmospheric flows than for water, as is the particle to fluid density ratio, so that particle impact and surface abrasion play a pivotal role in aeolian systems. As a consequence, work carried out on armoring in gravel bed rivers, for example, does not easily translate into useful analytical models for aeolian systems.

[3] During wind events, loose particles are winnowed from sediments containing coarse, non-erodible elements. This leads not only to a progressive increase in the aerodynamic roughness of the surface, but also, to an eventual increase in the wind speed needed to entrain particles into the airflow. Numerous studies have been carried out, both in the field and in wind tunnels [e.g.,Marshall, 1971; Nickling and McKenna Neuman, 1995; Wolfe and Nickling, 1996; Wyatt and Nickling, 1997; McKenna Neuman, 1998; Crawley and Nickling, 2003; Gillies et al., 2006; King et al., 2006; Brown et al., 2008], concerning shear stress partitioning on such rough surfaces. Much of the recent empirical work has been focused upon rigorous testing of a theoretical model describing the partitioning of the total stress (τ) between that acting on the protruding roughness elements (τr) and the intervening bed surface (τs),

display math

This concept was introduced by Schlichting [1968] but later refined by Raupach [1992] and Raupach et al. [1993] to provide a model for the prediction of sediment entrainment, as given in its original form below

display math

Rt refers to the square root of the shear stress ratio, which represents the proportion of the total stress that is partitioned to the stress acting on the intervening bed surface (τts) at the threshold for particle entrainment. An alternative and perhaps simpler interpretation for 1/Rt is that it represents the proportion by which the friction velocity required for particle entrainment from a rough surface (u*t) exceeds that for the smooth, unprotected bed surface (u*ts). Underpinning this model is the key assumption that the silhouette size and shape of each roughness element determine the volume and planimetric extent of a wedge- shaped shelter zone formed to the lee. The roughness density (λ) is determined as the total frontal-silhouette area of all roughness elements divided by the total planimetric area of the surface in which they lie.β represents the ratio of the drag coefficient for an individual roughness element to that for the smooth, unobstructed surface (Cr/Cs), where Cs can be determined from τs/ρuh2 and uh represents the wind speed at top of an element of height, h. The ratio of roughness element basal area to frontal area (σ) is incorporated into the model such that σλ indicates the basal area index or the fractional coverage. According to Raupach et al. [1993], the m parameter (0 < m < 1) scales the maximum shear stress (τs) exerted at a given point on the exposed surface to the spatially averaged instantaneous shear stress (τs) acting on a surface with a lower roughness density, such that:

display math

with m ≈ 0.5 for a flat, erodible, homogeneous surface. On the whole, numerous studies carried out both in the field and in wind tunnels [e.g., Wyatt and Nickling, 1997; Crawley and Nickling, 2003; Gillies et al, 2006; King et al., 2006; Brown et al., 2008] have demonstrated that the Raupach model provides reliable predictions of the drag partition for arrays of roughness elements having uniform shape and size. A comprehensive review of such work is provided in Nickling and McKenna Neuman [2009], the details of which shall not be repeated herein.

[4] Apart from these fundamental contributions, a number of deficiencies remain in our treatment of armored beds in aeolian systems:

[5] 1) Natural roughness elements have considerably more complex shapes and spatial distributions than the idealized geometric forms upon which the shear stress partitioning model is based. Few measurements have been made of the micro-topography of armored surfaces in ‘real’ aeolian systems that include, for example, pebble and/or shell pavements on beaches.

[6] 2) The topography of the intervening bed that is adjusted to the preceding airflow/sediment transport conditions has been either largely ignored or treated with physically obscure parameters.

[7] 3) Shear stress partitioning is only one of several physical processes that govern the development of armored beds. Perhaps too much emphasis has been placed upon evaluating Rt at the expense of understanding and quantifying these phenomena.

[8] With regard to the first statement, not all roughness elements in the natural world are well approximated by ideal geometric forms, e.g., hemispheres, cubes and cylinders. Depending on their orientation for example, individual mollusc shells found within beach surfaces can be convex and aerodynamically smooth; concave with sharp, upturned rims presented to the wind; or blade-like when turned on their edge. Very little effort has been made to measure and develop suitable geometric indices for such elements. Only within the last several years have technological developments in high precision 3D laser scanning, GIS and remote sensing made rapid assessment of the topography of complex beds even possible.

[9] Second existing models of sheltering in aeolian systems focus primarily upon the fixed roughness element array, without much regard for adjustments in the intervening bed surface to the airflow and sediment transport conditions that created the armored surface. Such adjustments are recognized to alter the peak (spatial) surface shearing stress as approximated by the parameter m in the Raupach model. As noted above, a great deal of previous work has been carried out in attempting to quantify m for varied settings, usually indirectly via model calibration against measurements of Rt. In these studies, either the details of the topography of the intervening, loose bed have been ignored in the analysis, or the roughness elements have been ideally situated upon a flat plane (e.g., dowels and hemispheres mounted on plywood). Knowledge of the bed topography is important for estimation of the supply of sediment that is available for entrainment during a wind event of high velocity, exceeding that which created the existing armored surface.

[10] With regard to the suite of processes responsible for the armoring of a sedimentary deposit, particle entrainment by wind in the field and laboratory cannot be considered independent of the role of grain impact. While it is true that fluid drag (τs) is solely responsible for moving the very first grains which roll and are lifted from the bed, these immediately initiate the motion of others via momentum transfer upon collision with the surface, even within areas of the bed considered to be sheltered from the fluid flow. Researchers who routinely measure entrainment phenomena recognize that in practice there is no clear separation between the fluid and impact thresholds [e.g., Nickling, 1988] as originally envisioned by Bagnold [1941]. With regard to armored beds, some particles participate in highly energetic rebounds from the tops of the roughness elements which can contribute to a momentary increase in the transport rate beyond that for an unsheltered surface [McKenna Neuman and Nickling, 1995; McKenna Neuman, 1998]. Other particles may either roll and become trapped against the upwind face of a roughness element, or change the course of their trajectory in rebounding (from collision with the element) in a spanwise or upwind direction. In the case of mollusc shells, a fraction of the population of saltating particles is captured within the cavities created by their complex geometric forms.

[11] Finally, for aeolian systems in particular, no detailed measurements have been published with regard to adjustments in (i) turbulence intensity, structure and spectra, (ii) Reynolds stress, and (iii) the total kinetic energy that take place during armoring. It is now well recognized from experiments carried out in both fluvial and aeolian systems that sweep/burst structures play a pivotal role in sediment entrainment. Given the large differences between the properties of the two fluids (water and air), it is not acceptable to assume that the details of these findings readily translate between geophysical systems.

[12] In response to the deficiencies outlined above, this paper reports on a series of wind tunnel experiments which address the development and structure of mollusc shell pavements formed on beach surfaces. Apart from the relatively simple observations carried out more than thirty years ago by Carter [1976] and Carter and Rihan [1978], no geomorphologist has attempted to quantify the degree to which coastal beaches may be protected by the formation of these pavements, although they are found world-wide. These armored surfaces possess a highly complex micro-topography, while the roughness element form and size is easily manipulated, and so, they are particularly well suited to the core objectives of our experiments, which are listed as follows:

[13] 1) To develop and carry out a methodology for making detailed 3D micro-morphometric measurements of surface armoring in an aeolian system.

[14] 2) To measure the wind speed, and from this determine the fluid shear stress, required for particle entrainment from surfaces of systematically altered roughness morphology in order to isolate and compare the varied geophysical mechanisms identified with armoring.

[15] 3) To measure the localized topographic adjustment of the intervening bed surface for varied wind speeds, and from this, estimate the volume of sediment available for entrainment.

2. Methods

2.1. Test Surface Materials and Preparation

[16] Commercial grade mollusc shells were tumbled in a cement mixer along with water and bleach to clean and sanitize them. They were then air-dried and sieved into two size fractions: small (<12.7 mm) and large (≥12.7 mm). This division was arbitrary and based on visual appearance. The shells then were added to medium, well sorted sand (mean diameter 280μm or 0.49 ϕ, standard deviation 0.71 ϕ, skewness −0.32 ϕ) to attain either 1:4 (shell:sand) or 1:2 concentrations by volume (Table 1). Large amounts of these mixtures were returned again to the cement mixer, tumbled to prevent sorting, and then dumped evenly onto the wind tunnel floor and levelled by hand. Atypical particles, perched precariously on the test bed, were blown away at a low wind speed prior to commencement of the formal experiment.

Table 1. Summary of Threshold Test Data by Varied Surface Type as Defined by the Volumetric Ratios of Shell to Sand
Shell:Sand by Volumeu∞t (m s−1)u*t (m s−1)zo × 10−5 (m) σλλh (mm)
Sand
05.50.264 nanana
 
Crushed Shells
1:86.20.326avg0.1170.0181.17
    min0.0850.0151.05
    max0.1320.0221.28
1:46.80.4220avg0.2170.0341.42
    min0.1490.0141.11
    max0.3010.0441.64
 
Small Shells
1:46.60.371avg0.1660.0523.54
    min0.0880.0272.66
    max0.0260.0804.66
1:27.60.526avg0.4330.0954.80
    min0.2190.0833.49
    max0.5060.1075.66
 
Large Shells
1:46.40.416avg0.1400.0637.27
    min0.1250.0416.14
    max0.2040.0888.44
1:27.10.5616avg0.3050.1188.23
    min0.2570.1097.08
    max0.3450.1309.21

[17] Many natural beaches contain an abundance of shells that have been pounded and thus fractured in the surf. While their effect on shear stress partitioning may be much reduced as compared to experiments involving whole shells, which protrude up to several centimeters into the boundary layer flow, shell fragments in the same volumetric concentration primarily reduce the supply of loose sand particles available in the surface matrix. This presents a need to design a set of experiments that allow for comparison of these influences (i.e., drag partitioning versus particle supply limitation). After the first set of wind tunnel runs was completed, therefore, a second set was repeated using crushed shells. The whole shells were reduced to fragments (i.e. ‘flattened’) by crushing them in a press. Fragments exceeding an arbitrarily selected diameter of 6.35 mm were discarded, while ones finer than this cut off value were isolated by sieving and combined with the test sand in concentrations of 1:4 (shell: sand) and 1:8. High concentrations of shell fragments (e.g., 1:2) resulted in excessive coverage of the test bed, and so, they were not used in testing.

2.2. Wind Tunnel Facility and Instrumentation

[18] All experiments were carried out in a straight line, suction type wind tunnel at Trent University. The working section is 13.8 m in length (X) and 0.71 m in width (Y), with a floor to ceiling height (H) of 0.76 m. For the natural development of a boundary layer wind profile, White and Mounla [1991]suggest that X/H ≥ 5. In the Trent tunnel, this criterion is met 4 m beyond the entrance to the working section, so that a little more than two-thirds of the bed in the tunnel is immersed in a deep boundary layer flow without any intervention to ‘trip’ or initiate shear. As for most wind tunnels, we improve on this performance by mounting a roughness array (e.g., staggered wooden dowels) at the entrance to the working section so that shear is introduced in the flowbefore reaching the test bed. The depth of the clean air boundary layer (δ) is typically in the order of 0.25–0.30 m in the Trent tunnel, giving X/δ ≅ 50, which just meets the stringent requirements for equilibrium flow stipulated by White and Mounla [1991]. Motor speed is adjusted by a microprocessor-based programmable motor drive. Extreme values of the freestream velocity (u) sampled at 10 Hz vary by only 2% from the 10 min mean.

[19] Vertical profiles of wind speed (24 positions, 5 mm < z < 40 mm) were obtained at three stream wise positions (x = 2.5, 5.55 and 10.15 m; x/H = 3.3, 7.3 and 13.2, where H is the working section height) via micro pitot tubes (1 mm inner diameter) mounted on traverse assemblies. From the standard Prandtl-von Karman wind profile equation, these measurements provide estimates of the friction velocity (u*), roughness length (zo), and where appropriate, the zero plane displacement (d). A 2D laser Doppler anemometer (LDA) also collected vertical profiles of wind velocity, particle velocity, Reynolds stress and turbulence intensity during the tests, as required for a companion study.

[20] The topography of each surface was measured using a 3D Konica Minolta Vivid9i laser scanner. The instrument, with a wide-angle 8 mm lens suitable for use in this study, had a resolution of approximately 250μm in depth (i.e., ∼ grain scale), and 500 μm in the horizontal plane. The total area of bed surface captured in a given scan was 0.13 m2, about 1.3% of the total test surface area. Each sampling period is represented by three scans obtained along a wind aligned transect at 1.5, 4.0 and 7.5 m from the upwind edge of the test bed. The very large size of the test bed, the high precision of the scanner, the geometry of the tunnel cross section, and the imposition of the fixed tunnel roof, made it impossible to scan the whole of the bed surface.

[21] Owing to the complexity of the roughness element shape that is superimposed on an undulating surface, determination of the shell coverage, height distribution and roughness density is a formidable task. For example, the shells are similar in color to the sand, so that boundary detection is difficult. Strings and clusters of roughness elements are easily misinterpreted as a single shell of disproportionate size. From the digital elevation data obtained, it was necessary therefore to first identify all local maxima, each one ideally representing a discrete shell residing within the surface, whether isolated or situated within a cluster. From these maxima, shell and non-shell areas were then distinguished using a set of rules based upon an appropriate cutoff height for each sample type (e.g., small shells as compared to large shells). Further details concerning the algorithm employed in the analysis of the digital elevation data are provided inAppendix A.

2.3. Threshold Testing

[22] Threshold testing on unadjusted, ‘man-made’ surfaces preceded transport testing. For each experiment, the bed surface topography was scanned immediately before the wind tunnel was started. Following this, the freestream velocity (u) in the core of the wind tunnel airflow was stepped up gradually until the cumulative number of particle counts recorded by a piezoelectric impact sensing device (Sensit™) began to ramp up steadily (Figure 1). Care was taken to mount the bottom of the sensor ring flush with the bed surface, such that undetected particles did not impact below the sensor. The freestream velocity recorded before the onset of this continual increase in particle motion was identified as representing threshold (u∞t), as demonstrated in the example shown in Figure 1. Since aeolian entrainment is caused by both fluid drag and impact/ejection, a cascade occurs along the fetch of the wind tunnel, so that there generally is not a perfect coincidence in threshold identified among all three Sensits™ positioned at x = 3.25, 6.10, and 9.42 m from the upwind edge of the test bed. In select experiments, threshold was identified where at least two of three Sensits™ recorded a steep, synchronous incline in the cumulative particle count, as compared to a third Sensit™ that demonstrated a similar incline either at an earlier or later velocity step. In any event, the experimental determination of threshold is associated with a degree of subjectivity, even in highly controlled wind tunnel settings. This is particularly true for spontaneous but non-sustained flurries of motion that occur for natural distributions of particle size, shape and packing at low wind velocities.

Figure 1.

Temporal variation in the cumulative number of particle counts recorded by three Sensits™, at varied positions along the wind tunnel working section, as the freestream velocity was stepped up. The velocity step before the continuous rise in the number of particles entrained marks the threshold condition, which in the example shown is 6.25 m s−1.

2.4. Transport Testing

[23] Once u∞t was determined for the unadjusted bed, the wind speed was set to 8 m s−1 so that sand particles were entrained and transported over the whole of the bed surface. The Sensits™ were removed for this test, as their bluff bodies caused perturbations in the airflow and the particle saltation pathways. A vertical, isokinetic sediment trap at the down wind end of the tunnel working section collected and weighed particles each second. With the progression of time at this wind speed, the supply of particles available within the intervening sand bed between the shells was depleted, so that the transport rate dropped to a negligible value (<0.05 g cm−1 s−1). This typically occurred after one to two hours of wind tunnel operation. The test then was terminated. All bed materials were removed, completely remixed, poured back into the tunnel, and finally, levelled. The entire test protocol was repeated again; this time at a higher velocity setting, incremented by 1 m s−1 in u for a total of 5 sequential experiments. Since the volume of sediment winnowed from each test surface represented less than 0.02% of the volume of the entire sand bed, it is assumed that upon complete remixing, no change in the particle size distribution of the intervening sand surface occurred from test to test.

[24] Immediately before and after each of these experiments, the bed surface topography was scanned at three positions (center point x = 0.80, 3.9, 7.35 m from the upwind edge of the test bed) to determine both the volume of sediment lost, and any changes in the fractional coverage (σλ) and roughness density (λ) of the exposed shells. On select beds, both erosion and deposition were noted to occur in small areas in the vicinity of the roughness elements while the sand surface adjusted to the airflow and particle transport conditions. Herein, these are referred to as adjusted beds in recognition of the fact that not only is the shell topography important in the consideration of shear stress partitioning, but also, the intervening sand bed topography plays a role as well. In this paper, the fully adjusted, stable bed produced at the termination of each transport test is considered to have its own threshold velocity (u∞t), equivalent to the velocity setting at which the transport test was run. That is, no further particles could have been removed from the bed, unless the wind velocity was increased beyond this level.

3. Results

3.1. DEM Analysis

[25] As a frame of reference, Figure 2 displays photographs of select surfaces obtained prior to transport tests run at u = 12 m s−1 (Figure 2, left), as compared to those captured at the termination of each experiment when the surface armoring was sufficient to prevent further particle entrainment (Figure 2, right). In all cases, the number of shells appearing on each surface increases substantially with their excavation from the deflating bed. In select instances, the shells have an altered orientation after some period of time, while some have rolled along the surface, eventually coming to rest against others downwind. Of particular note is the observation that the shells are not randomly distributed throughout the viewing area, despite all efforts to ensure uniform mixing of the materials loaded into the bed of the tunnel. Instead, they are semi-organized into chains and clusters with the long axis of many of the shells appearing to be aligned top to bottom or with the airflow in the tunnel. This rough alignment may have been created in part during levelling of the bed in which a straight edge was dragged over the surface toward the terminus of the working section.

Figure 2.

Images of bed surfaces from the scanner. Black arrow indicates wind direction. Top row refers to crushed shells, the middle to small shells and the bottom to large shells, all in a 1:4 (shell:sand) concentration by volume. (left) Beds created before exposure to airflow and particle transport at 12 m s−1. (right) The same beds after each test when particle emission had dropped to a trivial level. The white arrows in the lower right image point to evidence of morphometric adjustment, e.g., a sand tail for the dashed line and a deflation well for the solid line.

[26] On the whole, classic patterns of erosion and deposition associated with coherent flow structures that form in the vicinity of isolated roughness elements are not pervasive in these images. A close investigation of the sand surface surrounding several of the large shells after transport shows that is sculpted into lee-side sand tails (e.g., dashed white arrow inFigure 2 (bottom right)). Troughs that surround the upwind faces of a just few shells (e.g., solid white arrow in Figure 2) could be associated with either the presence of stationary horseshoe vortices or particle ricochets off the bluff body.

[27] Probability distributions of shell height (Figure 3) are provided for topographic scans obtained prior to the transport tests (top row), and afterward (bottom row), for all forms of roughness element in 1:4 concentrations. The distributions are typically unimodal and skewed toward the right tail; that is, relatively large heights are observed before and after wind tunnel testing in each population of shells considered. The mean heights of the roughness elements contained in each of the adjusted beds shown in Figure 3 were 1.7, 4.3, and 7.7 mm for the crushed, small and large shells, respectively. None of the bed types studied at varied concentrations demonstrate a consistent increase in the amount of shell protrusion above the mean bed surface over time.

Figure 3.

Distribution plots of roughness element height before and after sediment transport, corresponding to the top and bottom rows, respectively. Height data refer to the surfaces shown in Figure 2 (1:4 concentration, u = 12 m s−1, x = 7.4 m).

3.2. Threshold Model Validation

[28] A quadratic function (Figure 4) well describes the influence of the fractional shell coverage (σλ) upon u∞t, irrespective of the type of shell material added to each sand bed. Herein the freestream wind speed (u) rather than friction velocity (u*) is employed since the former is a controlled variable, while the later is an outcome that depends upon changes in the aerodynamic roughness length (zo) and Reynolds stress. Notably all surfaces represented in Figure 4 are topographically unadjusted to the airflow; that is, there has been no history of sediment transport on these beds. It appears from this perspective that a large volumetric concentration of shells within the bed surface simply gives rise to a large value of σλ, and thereby u∞t, while the shell size and thereby height appear to be of somewhat lesser importance. This is especially true of the 1:4 experiments with crushed shells which demonstrate a greater u∞t than either the large or small shell pavements at the same volumetric concentration. These relatively flat though numerous shell fragments essentially ‘paved’ a greater proportion of the bed surface, σλCS = 0.22, than either surface containing whole shells, e.g., σλLS = 0.14 and σλSS = 0.17 (Table 1). The problem with this appealingly simple relation is that extrapolation beyond the range of experimentation is questionable. As for example, given σλ = 1 whereupon by definition there is no supply of loose sand particles to entrain, u∞t is predicted to increase to 7.4 m s−1. This is obviously unrealistic.

Figure 4.

Variation in threshold (freestream) velocity as a function of the fractional coverage of the roughness elements contained within the bed surface.

[29] The theoretical stress partitioning model, which in effect relates the shear stress ratio (Rτ = τ/τts = u*2/u*ts2) to (1 + mβλ)⋅(1 − mσλ), avoids many of the pitfalls of an empirically based treatment but introduces variables having increased uncertainty in their measurement (i.e., u* rather than u; and λ rather than the fractional coverage). For measurements of Rτ and λ obtained for the unadjusted surfaces, shown in Figure 5a and reported in Table 1, equation (2) was forced through all seven data points by assuming a standard value for m ≅ 0.5 [Raupach et al., 1993] and iteratively varying β, which was determined to provide the best fit with a value ≅ 130. We note that given the inconsistent shape and orientation of the shells within the bed surface, direct measurement of a representative drag coefficient (Cr) for any given roughness element is impossible in this context. The parameter σ varied between bed types (2.3 ≤ σ ≤ 6.2), with lowest values for the large whole shells and highest for the crushed shells. As expected, the initial concentration of shells also strongly governs λ, with highest roughness densities represented in the 1:2 mixtures. Larger shell sizes also contribute to larger λ values. The measurement data confirm that for all bed surfaces examined, the proportion of the total shear stress partitioned to the surface is very strongly governed by the roughness density, as assumed in the Raupach model.

Figure 5.

(a) Shear stress ratio (Rτ) at threshold as a function of the roughness density (λ). Note that these surfaces are unadjusted to any given airflow. (b) The same relation as in Figure 5a but for surfaces that are adjusted to the airflow condition through the transport of sediment.

[30] In comparison, Figure 5b presents the results from experiments carried out on test beds with the same shell contents as in Figure 5a, but which differ from these in the adjustment of the topography of the intervening sand bed surface to varied wind speed and sediment transport conditions. On the whole, the shear stress ratio Rτ remains positively correlated with roughness density, but there is far greater scatter in this plot than in Figure 5a for the unadjusted or planar sand beds. As a rule of thumb for each bed surface type, increasing values of Rτ represent exposure to increasing wind speeds, often with increasing amounts of sand transport and topographic adjustment occurring before the particle supply is exhausted and a new entrainment threshold is established. For example, data for the surfaces exposed to particle transport at the lowest wind speed settings (8 ≤ u ≤ 9 m s−1) are represented in the plot as values for which Rτ < 4. In the case of the crushed shell beds, the adjustment in λ with increasing wind speed (2 < Rτ < 6) is small, suggesting that not only were tiny amounts of sediment moved but also that the shell concentration had little to no influence. In contrast, test beds containing whole shells in a 1:4 concentration demonstrate large increases in the roughness density associated with deflation of sand from the intervening bed and the consequent excavation of the shells. The data for whole shells in 1:2 volumetric concentrations are particularly interesting in that no matter the fluid stress to which the surface has been exposed, or the amount of sediment transport, no systematic change is observed in λ with Rτ.

[31] The average σ value is different for each adjusted surface represented in Figure 5b, so that it is impossible to plot a best fit model based on equation (2), similar to that shown in Figure 5a. However, given a midrange value of σ = 4.2, representing the data set in its entirety, it is instructive to investigate how adjustments in the parameters m and β affect the fit of the Raupach model to the data set as a whole. Parameter values (m = 0.4 and β = 130) that are similar to those describing the topographically unadjusted surfaces (Figure 5a) produce a model fit that closely follows the lower boundary of the data cloud. This would seem reasonable since the wind speed, and thus fluid shear stress, involved in each experiment was sufficiently low that little particle entrainment and topographic adjustment occurred (i.e., similar form to the unadjusted bed). Rough fits of the Raupach model with arbitrary values of m = 0.8 and β = 170 (medium dashed line) and m = 1 with β = 200 (short dashed line) run through the center and along the upper boundary of the data cloud, respectively. Increasing values of the parameter m, suggest greater uniformity in the distribution of fluid stress established across the intervening sand bed, whereas a value of unity for m suggests that τs = τs as in equation (3), Raupach et al. [1993]. Recent (unpublished) work carried out in the Trent wind tunnel confirms that with adjustments of the bed surface topography during particle entrainment and transport, particularly in the vicinity of leeward wake zones, spatial perturbations in the bed level shear stress either diminish or disappear altogether.

[32] In examining the aggradation/degradation plots in Figure 6, it appears that only in the case of the 1:2 surfaces is the total amount of localized sediment accumulation roughly balanced by that lost in other places on the bed surface. This would suggest not only that there should be no net change in λ, but also that substantial sculpturing of the bed surface occurred, perhaps with the effect that the mean shear stress increased at the expense of perturbations across the surface (i.e., m → 1). With regard to both the small and large shells in a 1:4 concentration (Figure 6), increasing deflation of the armored bed with increasing wind speed is matched, on the whole, with increases in the roughness density and shear stress ratio (Figure 5b). In the case of all transport experiments, however, it is also possible that particle scale armoring occurred, especially at the highest freestream velocities when presumably all but the coarsest sand particles were entrained from the bed surface by the end of the run. This alone could increase Rτ, independent of any morphodynamic effects.

Figure 6.

Summary of the local elevation change (Δz) relative to the original digital elevation model, plotted for each of six surface types tested at five freestream velocity settings. The sum of all elevation differences is plotted for each experiment, the black bar representing only those values associated with erosion (negative values), and the gray bar representing the remaining grid points sampled for which a gain in elevation was observed (positive values).

[33] In further support of the data describing topographic adjustments to the bed surface associated with sediment transport at wind velocities exceeding threshold, detailed maps are provided in Figure 7 of the elevation difference between the initial surface and the outcome. Each map refers to surfaces at a 1:4 initial concentration exposed to a 12 m s−1 wind until all available sediment that could be entrained was depleted.

Figure 7.

Maps of the distribution of either local erosion (negative values), or local deposition (positive values), for (a) crushed, (b) small and (c) large shells in a 1:4 concentration after exposure to an airflow of 12 m s−1. All dimensions are in mm. A value of zero (royal blue) indicates no change in the surface elevation, often representing shells, as compared to green and yellow which indicate erosion. Each plot refers to DEM data obtained for the streamwise position x = 7.40 m. Black arrow indicates wind direction.

[34] Starting with the crushed shells (Figure 7a), about half of the surface area was stripped of 2–5 mm of sediment. The remainder of the surface, which can best be described as clusters of exposed or interlocking shells, demonstrates essentially little to no change in elevation. The plot gives the clear impression that the roughness elements are not operating independently, but rather, display some degree of spatial organization that is not captured by the roughness density statistic (λ). The same can be said for the small shells (Figure 7b). In the case of the large shells (Figure 7c), there is less evidence of clustering than in the case of the crushed shell and small shell beds, while a large proportion of the surface appears unaltered by the airflow. However, the relative magnitude of surface elevation change is substantial in the small, isolated areas where it does occur. Some shells appear to have rotated and turned on their edges.

[35] Given the widely accepted conception that coherent flow structures play a role in stress partitioning, small amounts of net erosion are expected windward of each roughness element within the footprint of the horseshoe vortex, as compared to a wedge of particles captured and protected in the flow separation region immediately behind each element. This hypothesis is not generally supported by the evidence in Figure 7, wherein the sand bed appears to be protected within clusters of shells. Net erosion is confined to corridors of lower fractional coverage. In the lower third of the plot shown in Figure 7b, several discrete shells sitting within these corridors demonstrate increased sediment loss immediately adjacent to their upwind faces and along the sides, as consistent with horseshoe vortex development. However, a large majority of isolated shells does not demonstrate this pattern. Similarly, when the shells themselves are stripped from each plot (Figure 8), there is strong evidence that the adjusted topography is in large part a relic of the original sand surface.

Figure 8.

Sand surface topography (left) before and (right) after sand transport at wind speeds of 12 m s−1(x = 7.4 m). Black arrow indicates wind direction. All dimensions are in mm. Top row refers to the experiment involving the large shells in a 1:4 concentration and the bottom row to that for the small shells. The non-erodible roughness element elevations are stripped from these plots, with white assigned to the basal footprint of each shell.

3.3. Net Deflation

[36] There are few published data that support estimation of the net amount of sediment that can be eroded from rough surfaces for varied wind speeds. In the context of the present study, such data are potentially useful for coastal managers. In beach nourishment programs, for example, the inclusion of substantial amounts of shell material strongly influences sand entrainment and transport, as described by Van der Wal [2004]. The present study suggests that in settings where shells constitute approximately half of the volume of the beach, little to no net loss of sand from the surface can occur although it might be redistributed locally (Figure 9). This would seem to be an optimum condition for surface stabilization. In comparison, very little difference in surface deflation is apparent between the small shells (<12.7 mm diameter) and shell fragments when they constitute approximately 1/4 of the beach deposit. The net amount of sediment liberated from these surfaces is moderate, in the order of 2–4 kg m−2 at wind speeds of 12 m s−1 (Figure 9). Not surprisingly, crushed shells in a very low concentration (1:8) are poor with regard to surface protection at high wind speeds, liberating ≈7 kg m−2. The worst case scenario is a moderate 1:4 concentration of large shells (>12.7 mm diameter) which at high wind speeds can produce as much as 10 kg m−2.

Figure 9.

Influence of wind velocity on the net mass of material removed (shown as negative values) from a unit area of surface of a given roughness element type and concentration. The two positive values representing the large shell experiments in a 1:2 concentration correspond to a tiny, net accumulation of sand sampled within the sub plots. Since there is no source of sand external to the test bed, small positive values for Q must be balanced by deficits elsewhere on the surface.

4. Discussion

[37] The shear stress partitioning approach represents a paradigm in the examination of particle entrainment on rough, sheltered surfaces. A large number of studies have demonstrated that with suitable calibration of its parameters, principally m and β, the Raupach model can be forced to compare well with data collected from a wide range of settings over a broad range of scales. Nonetheless, the wake structures conceptualized in the model are highly idealized, and certainly in the context of the present study, do not describe the complexity of natural surfaces. On this account alone, it can be argued that the model is of somewhat limited value as a foundation for understanding the formative geophysical processes governing armoring in aeolian systems.

[38] The high degree of correlation (r2 = 0.996) demonstrated between the fractional coverage of the shells on unadjusted surfaces and the free stream wind speed at threshold (Figure 4) is unexpected, given the rather deceiving simplicity of the relation. In the case of the 1:4 beds, u∞t increases in proportion to slight increases in σλ, but decreases with the element height, i.e., u∞t (crushed shell) > u∞t (small shell) > u∞t (large shell). The same is true for the 1:2 concentrations and would seem to be counterintuitive, given the demonstrated importance of aerodynamic sheltering on rough surfaces. However, the total fluid stress (ρu*t2) at the threshold for particle motion depends not only on u∞t, but also on the aerodynamic roughness length (zo), which on average appears in this study to be about 0.13h, where h is the roughness element height. That is, substitution of 0.13h for zointo the Prandtl-von Karman wind profile equation determines the effect on the fluid stress as follows

display math

where k is von Karman's constant (∼0.41) and ρ is the air density. Values of τ derived from equation (4) give Rτ (crushed shell) < Rτ (small shell) < Rτ (large shell), which is in full agreement with the order shown in Figure 5a.

[39] As suggested in Raupach's [1992] stress partition model, the shear stress ratio Rτ can be determined by multiplying (1 + βλ) by the proportion of the total surface area that is not occupied by the non-erodible roughness element (1 −σλ); that is, the proportion of the test bed in the present study covered with sand or As/A. The partitioning of the fluid force between the roughness elements and the intervening surface (Fr/Fs) is represented in the Raupach model as

display math

where Af is the element frontal area, so that (1 + βλ) then indicates the ratio of the total fluid force to that exerted directly on the bed surface (F/Fs). As FAs /FsA gives τ /τs, it becomes obvious that for situations where either Cr or Af (or both, i.e., crushed shells lying flat) are relatively small, variations in the fractional coverage of the roughness elements attain greater importance in the Raupach model, and visa versa. Figure 10 compares the relative influence of (1 + βλ) and (1 − σλ) in the context of the unadjusted beds, as related to Figures 4 and 5a. An increase in the concentration of small shells from 1:4 to 1:2, for example, decreases the proportionate area of the intervening bed surface (1 − σλ) by a factor of 1.46 from 83% to 57%. Because of the corresponding increase in the roughness density that also occurs, however, (1 + βλ) increases by a factor of 1.75 from 7.5 to 13.1. The outcome is a 19% increase in Rτ when the concentration of small shells is doubled, a trade off between reductions occurring in both the fluid force partitioned to the intervening bed surface and the area of sand exposed.

Figure 10.

Components of the fluid stress ratio (Rτ) at the threshold for particle motion.

[40] Independent of the shear stress partitioning approach, there may be a further explanation for the demonstrated dependency upon the roughness density. The bluff bodies of the roughness elements were visually observed to interfere with, and frequently block, the cascade of intermittent particle rolls, slides, and hops that lead to the inception of sustained mass transport. Further investigations of this process are greatly needed.

[41] In the case of the adjusted beds, the roughness density as determined by the frontal area of the shells has no bearing on the stress ratio at threshold when the concentration of elements is high (1:2). Instead the mobile fraction of the bed is sculptured by a modest amount of sediment redistribution without net loss and thereby, alteration of λ.This mechanism is not explicitly accounted for in the Raupach stress partition model with its sole focus upon the geometry of the non-erodible elements. When considering the armoring of natural surfaces, the discovery that adjustments in the topography of the erodible fraction of the bed are of paramount importance adds another level of complexity. It suggests that the undulating bed surface and the non-erodible elementstogether constitute the form roughness, particularly when there is a high concentration of elements present in the deposit.

[42] The observation that the non-erodible roughness elements also do not act in isolation in most cases, but sit within clumps and strings, is similar to the case of vegetation growing on rangelands for which for which sediment transport is routed through the intervening corridors [e.g.,Okin, 2008]. Indeed, for surfaces with many clusters of shells (shells with their boundaries connected), the frontal area for each individual shell cannot be obtained from the methods outlined in Appendix A; that is, the cluster is considered as one single shell. While this approximation may affect the accuracy of the roughness parameter calculation and is sensitive to the cut-off value, we believe this treatment is reasonable since the effect of clustered shells on the fluid stress should be significantly different from the summation of the effect from each individual shell. Clearly, there is a great need for the development of new parameters which suitably represent the full topographic perturbation of the adjusted bed surface as relevant to the fluid dynamic adjustment that occurs in response.

[43] Finally, sand particles entrained and traveling near the bed surface do not follow turbulent perturbations in the airflow pattern, owing to the large particle to fluid density ratio and thereby their relatively large momentum. Unlike the case of large clumps of vegetation in desert regions or boulders in rivers, saltating particles can hop over shells lying on beaches and similarly sized roughness elements of any type. As also explained in the early work of McKenna Neuman and Nickling [1995] and McKenna Neuman [1998], relatively elastic collisions with non-erodible roughness elements give rise to high energy ricochets that are steered by the roughness element geometry, so that it is entirely possible for ejections to occur within areas that might otherwise be treated as sheltered from the airflow. It therefore is suggested that patterns of entrainment and deposition on an armored surface are mainly driven by particle splash in aeolian systems, rather than by fluid drag and coherent flow structure.

5. Summary

[44] The experiments reported in this paper provide a frame of reference that is potentially valuable to modellers and coastal managers alike. The concentration of non-erodible roughness elements in a given sedimentary deposit is of paramount importance to its long-term stability and the conditions required for stabilization. Where one quarter (or less) of the sediment volume is occupied by shells, moderate to severe erosion will occur by continued excavation, although for elements under ≈13 mm in diameter, the effect of the roughness element diameter can be ignored in most cases. Worst-case erosion occurs for large roughness elements exceeding 13 mm in diameter. For beach deposits where non-erodible shells represent half of the volume of the parent material, the surface is highly stable from the outset. Although some reworking of the intervening, erodible sediment occurs, no net erosion or deposition takes place on these surfaces. With deflation of beds having low volumetric concentrations of non-erodible roughness elements, the fractional coverage on the surface will eventually exceed ∼30% such that the entrainment of the loose fraction will drop to insignificant amounts for most natural wind speeds.

[45] With a suitable selection of several parameter values, the Raupach shear stress partitioning model can be optimized to provide reasonably good predictions of the friction velocity required to entrain sediment from complex, armored surfaces. However, it is impossible to prove that such values (e.g., m and β) make physical sense in this particular context. Direct measurement of the roughness density is a formidable task, even when high resolution digital elevation data are attainable. Given that the roughness element height is demonstrated in this study to play a lesser role than basal area, the large expenditure of resources required to determine λbecomes difficult to justify. Although the approach developed in decomposing and analyzing the surface topography may well be useful for other applications, it is likely sufficient to consider only planimetric data in studies addressing armoring via deflation. Since in practice, particle entrainment by fluid drag is inseparable from that by impact in aeolian systems over the short spatial and temporal scales considered in this study, stress partitioning should be regarded as just one of a suite of geophysical processes involved. Similarly, topographic adjustments in the erodible surface are demonstrated in this study to be of the same magnitude as non-erodible roughness element width and height, and generally, they do not adopt a form suggestive of flow separation in relation to a discrete roughness element. As such, they need to be given much more attention in future work.

Appendix A

[46] This appendix lists the steps followed to measure shell height, coverage and roughness density (λ) from digital elevation models obtained using a 3D laser scanner. By classifying the images into shell area and non-shell area based on local relief, the coverage can be easily calculated. The observation that many shells lie in contact with one another within clusters and strings, however, brings much difficulty to the task of discriminating between shells and obtaining the height of each one. As a consequence, an extended-maxima transformation and more conservative criteria were used to isolate the peak area of each individual shell from which its height was obtained.

[47] Step:

[48] 1. Obtain a photograph, Figure A1a, and a topographic scan of the test surface. (Because all elevations are referenced from the level of the scanner positioned above, the values in the digital elevation model in Figure A1bare negative. The center of the image is a fixed point, also called the sub-scanner point.)

Figure A1.

Algorithm for estimating shell height, coverage and roughness density. (a) Photographic image obtained from the scanner of a surface of small shells at a 1:4 concentration prior to threshold testing. (b) Digital elevation map after re-sampling the original 3D image. (c) Binary image of peaks (white) and non-peaks (black). (d) Binary image of shells (white) and non-shells (black). (e) Digital elevation map relative to new reference level. (f) Negative values set to zero. (g) Peak patch topography. (h) Shell patch topography. Units are in mm. Black arrow indicates wind direction.

[49] 2. To increase computing speed, the digital elevation model may be resampled to 1 mm × 1 mm resolution. Fill the holes (if any) in the digital elevation model using a cubic interpolation, Figure A1b.

[50] 3. Use the extended-maxima transform algorithm [Soille, 1999, pp. 170–171] within Matlab R2010 to select all regional maxima (i.e., the roughness element peaks). The cut-off heights (h1) in the present study were set as follows: Large Shells-1.25 mm, Small Shells-0.5 mm and Crushed Shells-0.3 mm. Inside the peak area, the relative height is smaller than h1. Set the non-peak grids to zero and peak grids to one,Figure A1c. Note that the white patches correspond to the peaks of the roughness elements. In short, this algorithm was able to separate all clustered shells, which allows calculation of the height of each individual shell.

[51] 4. Shell and non-shell areas also can be distinguished using the extended-maxima transform algorithm, with the cutoff heights (h2) set as h2 = 2h1. The non-shell grid value is set to zero and shell grid value to one,Figure A1d. Note in this case, clustered shells are observed. Shell coverage is calculated from the shell area divided by the full plane surface area.

[52] 5. The non-shell mean surface is treated as a new reference level. However, due to the non-uniform and unsteady deflation of the surface (i.e., dependent upon location, time and wind speed), this secondary reference level is highly variable as compared to the original reference level which was fixed at the position of 3D scanner. The height relative to this reference level for each grid is calculated (Figure A1e), and grids with relative height smaller than zero are set to zero, Figure A1f.

[53] 6. Peak patch topography, Figure A1g, was obtained by multiplying Figure A1c by Figure A1f. Individual shell height is identified using the highest recalibrated elevation for each peak patch. Standard deviation and the average of all shell heights can then be calculated.

[54] 7. Shell patch topography, Figure A1h, was obtained by multiplying Figure A1d by Figure A1f. The topography of each shell patch is projected against the windward direction, so that the silhouette area can be calculated. The roughness λ is obtained from the total projected area divided by full plane surface area.

Acknowledgments

[55] This study was funded by an NSERC grant to C. McKenna Neuman. The authors wish to acknowledge the efforts of Stephen Morris who spent many months assisting with the wind tunnel experiments. Steven Sanderson provided key technical support. The authors are grateful for the efforts of three reviewers and two editors who provided insightful suggestions that lead to improvements in an early version of the paper.