A field study of mean and turbulent flow characteristics upwind,over and downwind of barchan dunes

Field‐measured patterns of mean velocity and turbulent airflow are reported for isolated barchan dunes. Turbulence was sampled using a high frequency sonic anemometer, deriving near‐surface Reynolds shear and normal stresses. Measurements upwind of and over a crest‐brink separated barchan indicated that shear stress was sustained despite a velocity reduction at the dune toe. The mapped streamline angles and enhanced turbulent intensities suggest the effects of positive streamline curvature are responsible for this maintenance of shear stress. This field evidence supports an existing model for dune morphodynamics based on wind tunnel turbulence measurements. Downwind, the effect of different dune profiles on flow re‐attachment and recovery was apparent. With transverse incident flow, a re‐attachment length between 2·3 and 5·0h (h is dune brink height) existed for a crest‐brink separated dune and 6·5 to 8·6h for a crest‐brink coincident dune. The lee side shear layer produced elevated turbulent stresses immediately downwind of both dunes, and a decrease in turbulence with distance characterized flow recovery. Recovery of mean velocity for the crest‐brink separated dune occurred over a distance 6·5h shorter than the crest‐brink coincident form. As the application of sonic anemometers in aeolian geomorphology is relatively new, there is debate concerning the suitability of processing their data in relation to dune surface and streamline angle. This paper demonstrates the effect on Reynolds stresses of mathematically correcting data to the local streamline over varying dune slope. Where the streamline angle was closely related to the surface (windward slope), time‐averaged shear stress agreed best with previous wind tunnel findings when data were rotated along streamlines. In the close lee, however, the angle of downwardly projected (separated) flow was not aligned with the flat ground surface. Here, shear stress appeared to be underestimated by streamline correction, and corrected shear stress values were less than half of those uncorrected. Copyright © 2011 John Wiley & Sons, Ltd.     

Reynolds stress and sand transport over a foredune

Reynolds shear stress (RS = –u′ w′) and sand transport patterns over a vegetated foredune are explored using three‐dimensional velocity data from ultrasonic anemometers (at 0 · 2 and 1 · 2 m) and sand transport intensity from laser particle counters (at 0 · 014 m). A mid‐latitude cyclone on 3–4 May 2010 generated storm‐force winds (exceeding 20 m s^–1) that shifted from offshore to obliquely alongshore. Quadrant analysis was used to characterize the spatial variation of RS quadrant components (Q1 through Q4) and their relative contributions were parameterized using the flow exuberance relation, EX_FL = (Q1 + Q3)/(Q2 + Q4). The magnitudes of RS and sand transport varied somewhat independently over the dune as controlled by topographic forcing effects on flow dynamics. A ‘flow exuberance effect’ was evident such that Q2 (ejection‐like) and Q4 (sweep‐like) quadrants (that contribute positively to RS) dominated on the beach, dune toe, and lower stoss, whereas Q1 and Q3 (that contribute negatively to RS) dominated near the crest. This exuberance effect was not expressed, however, in sand transport patterns. Instead, Q1 and Q4, with above‐average streamwise velocity fluctuations (+u′), were most frequently associated with sand transport. Q4 activity corresponded with most sand transport at the beach, toe, and stoss locations (52, 60, 100%). At the crest, 25 to 86% of transport was associated with Q1 while Q4 corresponded with most of the remaining transport (13 to 59%). Thus, the relationship between sand transport and RS is not as straightforward as in traditional equations that relate flux to stress in increasing fashion. Generally, RS was poorly associated with sand transport partly because Q1 and Q4 contributions offset each other in RS calculations. Thus, large amounts of transport can occur with small RS. Turbulent kinetic energy or Reynolds normal stresses (u′², w′²) may provide stronger associations with sand transport over dunes, although challenges exist on how to normalize and compare these quantities. Copyright © 2013 John Wiley & Sons, Ltd.     

Spatial variability of three‐dimensional Reynolds stresses in a developing channel bend

Experimental results of the mean flow field and turbulence characteristics for flow in a model channel bend with a mobile sand bed are presented. Acoustic Doppler velocimeters (ADVs) were used to measure the three components of instantaneous velocities at multiple cross sections in a 135° channel bend for two separate experiments at different stages of clear water scour conditions. With measurements at multiple cross sections through the bend it was possible to map the changes in both the spatial distribution of the mean velocity field and the three Reynolds shear stresses. Turbulent stresses are known to contribute to sediment transport and the three‐dimensionality inherent to flow in open channel bends presents a useful case for determining specific relations between three‐dimensional turbulence and sediment entrainment and transport. These measurements will also provide the necessary data for validating numerical simulations of turbulent flow and sediment transport. The results show that the magnitude and distribution of three‐dimensional Reynolds stresses increase through the bend, with streamwise‐cross stream and cross stream‐vertical components exceeding the maximum principal Reynolds stress through the bend. The most intriguing observation is that near‐bed maximum positive streamwise‐cross stream Reynolds stress coincides with the leading edge of the outer bank scour hole (or thalweg), while maximum cross stream‐vertical Reynolds stress (in combination with high negative streamwise‐cross stream Reynolds stress near the bend apex) coincides with the leading edge of the inner bank bar. Maximum Reynolds stress and average turbulent kinetic energy appear to be greater and more localized over the scour hole before final equilibrium scour is reached. This suggests that the turbulent energy in the flow is higher while the channel bed is developing, and both lower turbulent energy and a broader distribution of turbulent stresses near the bed are required for cessation of particle mobilization and transport. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental investigation of the impacts of coherent flow structures upon turbulence properties in regions of crescentic scour

This study examines the spatial distributions of third‐order moments of velocity fluctuations, the turbulent kinetic energy (TKE) fluxes, and the conditional statistics of Reynolds shear stress across the equilibrium crescentic scour structures generated upstream of short horizontal static cylinders. Detailed velocity data were collected using three‐dimensional (3D) micro‐acoustic Doppler velocimeter (ADV) across and within the equilibrium scour marks. The analysis reveals that the positive and negative values of third‐order moments associated with the level bed surface and the scour holes are directly related to coherent structures. The components of TKE flux are discussed for the near‐bed region of the level bed surface and scour holes in relation to sweep–ejection events. A cumulant‐discard method is applied to the Gram‐Charlier probability distribution of two variables to describe the statistical properties of the term u′w′. The conditional statistics of the Reynolds shear stress show a good agreement with the experimental data. The distribution of the joint probability density function in the near‐bed region changes cyclically along the scour hole depending on the bottom fluid velocity, which implies a change from upward to downward flux of momentum and vice versa. Both the ejection and sweep events at near‐bed points on the level surface are more important than within the scour region; and in contrast, both events are stronger for the scour marks than the level bed surface at the outer layer. Sweeps dominate over ejections for the scour hole induced by smaller diameter and ejections dominate for larger diameter. Copyright © 2013 John Wiley & Sons, Ltd.     

An experimental study on the ripple–dune transition

Flume experiments were conducted on different bed stages across the ripple–dune transition. As flow velocity increases, an initially flat bed surface (made of fairly uniform sandy material) is gradually transformed into a two‐dimensional rippled bed. With further increase in velocity, two‐dimensional ripples are replaced by irregular, linguoid ripples. As the average velocity necessary for the ripple–dune transition to occur is imposed on the bed surface, these non‐equilibrium linguoid ripples are further transformed into larger, two‐dimensional dunes. For each of these stages across the transition, a concrete mould of the bed was created and the flow structure above each fixed bed surface investigated. An acoustic Doppler velocimeter was used to study the flow characteristics above each bed surface. Detailed profiles were used along a transect located in the middle of the channel. Results are presented in the form of spatially averaged profiles of various flow characteristics and of contour maps of flow fields (section view). They clearly illustrate some important distinctions in the flow structure above the different bedform types associated with different stages during the transition. Turbulence intensity and Reynolds stresses gradually increase throughout the transition. Two‐dimensional ripples present a fairly uniform spatial distribution of turbulent flow characteristics above the bed. Linguoid ripples induce three‐dimensional turbulence structure at greater heights above the bed surface and turbulence intensity tends to increase steadily with height above bed surface in the wake region. A very significant increase in turbulence intensity and momentum exchange occurs during the transition from linguoid ripples to dunes. The turbulent flow field properties above dunes are highly dependent on the position along and above the bed surface and these fields present a very high degree of spatial variability (when compared with the rippled beds). Further investigations under natural conditions emphasizing sediment transport mechanisms and rates during the transition should represent the next step of analysis, together with an emphasis on quadrant analysis. Copyright © 2001 John Wiley & Sons, Ltd.     

Turbulence characteristics of flow region over a series of 2-D dune shaped structures

This paper addresses the development of a flow region associated with turbulence and stress characteristics over a series of 2-D asymmetric dunes placed successively at the flume surface. Experiments were conducted over twelve asymmetric dunes of mean length 32 cm, crest height 3 cm and the dune width almost as wide as width of the flume, using 3-D Micro-ADV at the Indian Statistical Institute, Calcutta. The variations of turbulence statistics along the flow affected by the wavy bottom roughness have been studied. Quadrant decomposition of the instantaneous Reynolds shear stress has been adopted to calculate the contribution of ejection and sweeping events in shear stress generation. The relative dominance of two events are found to contribute in a cyclic manner (spatially) in the near bed region, whereas such phenomenon seems to be disappeared towards the main flow.     

Suspended sediment concentration and the ripple–dune transition

Flume experiments were conducted in order to monitor changes in flow turbulence intensity and suspended sediment concentration at seven stages across the ripple–dune transition and at three different positions above the bed surface. Three‐dimensional velocity measurements were obtained using an acoustic Doppler velocimeter (ADV). Suspended sediment concentration (SSC) was monitored indirectly using ADV signal amplitude. Although limited to time‐averaged parameters, the analysis reveals that SSC varies significantly with stage across the transition and with sampling height. The statistical analysis also reveals an apparent uniformity of suspended sediment concentration with height above the bed in the lower half of the flow depth at the critical stage in the transition from ripples to dunes. This is also the stage at which turbulence intensity is maximized. Statistically significant correlations were also observed between suspended sediment concentrations and root‐mean‐square values of vertical velocity fluctuations. These correlations reflect the various levels of shear‐layer activity and the distinct turbulent flow regions across the transition. Conversely, time‐averaged values of Reynolds shear stress exhibit a very weak relationship with suspended sediment concentrations. Copyright © 2004 John Wiley & Sons, Ltd.     

Airflow and roughness characteristics over partially vegetated linear dunes in the southwest Kalahari Desert

There is little understanding of the flow-field surrounding semi-vegetated linear dunes, and predictions of dune mobility are hampered by a lack of empirical data concerning windflow. In an attempt to characterize the near-surface airflow upwind of and over partially vegetated linear dunes in the southwest Kalahari Desert, this study presents measurements of vertical and horizontal wind velocity profiles across cross-sectional transects of seven partially vegetated linear dunes. Vegetation surveys combined with velocity measurements from vertical arrays of cup-anemometers, placed up to 2·3 m above the ground surface, were used to gain information concerning the modification of airflow structure caused by the intrusion of the dunes into the atmospheric boundary layer and to predict the variability of aerodynamic roughness (z₀) from interdune to crest. The results suggest an acceleration of flow up the windward slopes of the dunes and, as such, the data correspond to classical theory concerning flow over low hills (essentially Jackson and Hunt (1975) principles). Where the theory is incapable of explaining the airflow structure and acceleration characteristics, this is explained, in part, by the presence of a spatially variable vegetation cover over the dunes. The vegetation is important both in terms of the varying aerodynamic roughness (z₀) and problems concerning the definition of a zero-plane displacement (d). It is considered that any attempts to characterize surface shear stress over the Kalahari linear dunes, in order to predict sand transport and dune mobility, will be hampered by two problems. These are the progressively non-log-linear nature of the velocity profiles over the dunes caused by flow acceleration, and the production of thin near-surface boundary layers caused by areally variable aerodynamic roughness as a result of the partially vegetated nature of the dunes.     

Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel

Topographic interactions generate multidirectional and unsteady air?ow that limits the application of velocity pro?le approaches for estimating sediment transport over dunes. Results are presented from a series of wind tunnel simulations using Irwin‐type surface‐mounted pressure sensors to measure shear stress variability directly at the surface over both isolated and closely spaced sharp‐crested model dunes. Findings complement existing theories on secondary air?ow effects on stoss transport dynamics and provide new information on the in?uence of lee‐side air?ow patterns on dune morphodynamics. For all speeds investigated, turbulent unsteadiness at the dune toe indicates a greater, more variable surface shear, despite a signi?cant drop in time‐averaged measurements of streamwise shear stress at this location. This effect is believed suf?cient to inhibit sediment deposition at the toe and may be responsible for documented intermittency in sand transport in the toe region. On the stoss slope, streamline compression and ?ow acceleration cause an increase in ?ow steadiness and shear stress to a maximum at the crest that is double that at the toe of the isolated dune and 60–70 per cent greater than at ?ow reattachment on the lower stoss of closely spaced dunes. Streamwise ?ow accelerations, rather than turbulence, have greater in?uence on stress generation on the stoss and this effect increases with stoss slope distance and with incident wind speed. Reversed ?ow within the separation cell generates signi?cant surface shear (30–40 per cent of maximum values) for both spacings. This supports ?eld studies that suggest reversed ?ow is competent enough to return sediment to the dune directly or in a de?ected direction. High variability in shear at reattachment indicates impact of a turbulent shear layer that, despite low values of time‐averaged streamwise stress in this region, would inhibit sediment accumulation. Downwind of reattachment, shear stress and ?ow steadiness increase within 6 h (h = dune height) of reattachment and approach upwind values by 25 h. A distance of at least 30 h is suggested for full boundary layer recovery, which is comparable to ?uvial estimates. The Irwin sensor used in this study provides a reliable means to measure skin friction force responsible for sand transport and its robust, simple, and cost‐effective design shows promise for validating these ?ndings in natural dune settings. Copyright © 2003 John Wiley & Sons, Ltd.     

Experimental investigation on local shear stress and turbulence intensities over a rough non-uniform bed with and without sediment using 2D particle image velocimetry

The current work focuses on locally resolving velocities,turbulence,and shear stresses over a rough bed with locally non-uniform character.A nonporous subsurface layer and fixed interfacial sublayer of gravel and sand were water-worked to a nature-like bed form and additionally sealed in a hydraulic flume.Two-dimensional Particle Image Velocimetry(2 D-PIV) was applied in the vertical plane of the experimental flume axis.Runs with clear water and weak sediment transport were done under slightly supercritical flow to ensure sediment transport conditions without formation of considerable sediment deposits or dunes.The study design included analyzing the double-averaged flow parameters of the entire measurement domain and investigating the flow development at 14 consecutive vertical subsections.Local geometrical variabilities as well the presence of sediment were mainly reflected in the vertical velocity component.Whereas the vertical velocity decreased over the entire depth in presence of sediment transport,the streamwise velocity profile was reduced only within the interfacial sublayer.In the region with decelerating flow conditions,however,the streamwise velocity profile systematically increased along the entire depth extent.The increase in the main velocity(reduction of flow resistance)correlated with a decrease of the turbulent shear and main normal stresses.Therefore,effects of rough bed smoothening and drag force reduction were experimentally documented within the interfacial sublayer due to mobile sediment.Moreover,the current study leads to the conclusion that in nonuniform flows the maximum Reynolds stress values are a better predictor for the bed shear stress than the linearly extrapolated Reynolds stress profile.This is an important finding because,in natural flows,uniform conditions are rare.     

Examining the physical components of boundary shear stress for water‐worked gravel deposits

It is argued in this commentary that, in order to understand better the physical mechanisms that generate boundary shear stress over water‐worked gravel beds, flow velocity data should be re‐evaluated by spatial averaging the Reynolds equations to produce time‐ and space‐averaged (double‐averaged) momentum equations. A series of laboratory experiments were conducted in which the flow velocities were measured using a PIV system over two water‐worked gravel deposits. Combined with detailed data on the bed surface topography and vertical porosity, the physical components of shear stress were obtained. This enabled the various momentum transfer mechanisms present above, within and at the interface of a porous, fluvial deposit, to be quantified. This included the examination of the relevant contributions of temporal and spatial fluctuations in velocity and surface drag to the overall momentum transfer. It is demonstrated that double‐averaging represents a logical framework for assessing the fluid forces responsible for sediment entrainment and for investigating intragravel flow and sediment–water interface exchange mechanisms within the roughness layer in water‐worked gravel deposits. By considering the physical components of shear stress and their relative sizes it was possible to provide a physically based explanation for existing observations of enhanced mobility of gravel–sand mixtures and the transfer of solutes into porous, gravel deposits. This analysis reveals the importance of obtaining co‐located, high quality spatial data on the flow field and bed surface topography in order to gain a physical understanding of the mechanisms which generate boundary shear stress. Copyright © 2010 John Wiley & Sons, Ltd.     

Turbulence fields in the lee of two‐dimensional transverse dunes simulated in a wind tunnel

The turbulence field of airflow in the lee of a dune has significant impacts on dune dynamics and related processes. We used particle image velocimetry in a wind tunnel simulation to obtain detailed velocity measurements in the lee of two‐dimensional transverse dune models, then used the results to analyse their turbulence fields. The dune models used in this study had a single lee angle of 30°, and a total of six stoss angles: 3°, 5°, 10°, 15°, 20° and 25°. We used vorticity, turbulence intensity, Reynolds stress and turbulent kinetic energy to characterize the turbulence fields. These parameters were functions of stoss angle, wind velocity, distance from the dune crest and height above the ground surface. The stoss angles could generally be divided into two groups based on the profiles of mean velocity, turbulence and Reynolds stress. Stoss angles of 3° and 5° usually had similar profiles, and angles of 15°, 20° and 25° formed a second group with similar profiles. The profiles for the stoss angle of 10° were usually transitional and were intermediate between the two groups. Vorticity, Reynolds stress and turbulent kinetic energy increased monotonically with increasing free‐stream wind velocity, but their variations with respect to the stoss angle were complex. The stoss angles of 15° and 20° had the maximum values of these three parameters, thus these angles may have special significance in dune development given the characteristics of the mean velocity fields and turbulence fields they produce within the lee airflow. It is the streamwise velocity component and its turbulence that determine the surface shear stress. Copyright © 2008 John Wiley and Sons, Ltd.     

Measurements of Reynolds stress in a wind-driven lagoonal estuary

Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza     

Effects of turbulence on the transport of individual particles as bedload in a gravel‐bed river

This study investigates the association between mean and turbulent flow variables and the movement of individual particles in a gravel‐bed river. The experimental design implemented in the Eaton‐North River (Québec, Canada) is based on the simultaneous observations at a high temporal resolution of both particle movements as bedload using an underwater video camera and of the streamwise and vertical flow velocity components using a vertical array of three electromagnetic current meters (ECMs). The frequency and distance of displacement of particles larger than 20 mm that were sliding or rolling on the bed were measured from a 10 minutes long film. Mean and turbulent flow properties obtained for periods without sediment transport are compared to those when particles were sliding and rolling. When particles are sliding, weak differences are present for the mean streamwise velocity and normal vertical stresses. Instantaneous Reynolds shear stresses are significantly lower for sliding events which was not expected but could be explained by the important dominance of Quadrant 3 events (inward interactions). When particles are rolling, only the vertical normal stresses show a weak difference from those observed in the absence of transport but they tend to occur when Quadrant 2 (ejections) dominate the flow field. For both sliding and rolling particles, vertical and/or streamwise fluid accelerations show high magnitude values when compared to periods without transport. For sliding particles, streamwise acceleration is mostly negative and combines most of the time with a positive vertical acceleration. For rolling particles, streamwise and vertical acceleration are predominantly of opposite sign. These results suggest that fluid acceleration or deceleration in the streamwise and vertical directions is affecting the pressure field around particles. In this study, fluid acceleration seems to play a more important role than Reynolds shear stress or normal stresses for bedload movements. Copyright © 2010 John Wiley & Sons, Ltd.     

Modelling transverse dunes

Transverse dunes appear in regions of mainly unidirectional wind and high sand availability. A dune model is extended to two‐dimensional calculation of the shear stress. It is applied to simulate dynamics and morphology of three‐dimensional transverse dunes. In the simulations they seem to reach translational invariance and do not stop growing. Hence, simulations of two‐dimensional dune ?elds have been performed. Characteristic laws were found for the time evolution of transverse dunes. Bagnold's law of the dune velocity is modi?ed and reproduced. The interaction between transverse dunes led to the interesting conclusion that small dunes can travel over bigger ones. Copyright © 2004 John Wiley & Sons, Ltd.     

Variable and conflicting shear stress estimates inside a boundary layer with sediment transport

This paper presents a comparison between two methods for estimating shear stress in an atmospheric internal boundary layer over a beach surface under optimum conditions, using wind velocities measured synchronously at 13 heights over a 1.7 m vertical array using ultrasonic anemometry. The Reynolds decomposition technique determines at‐a‐point shear stresses at each measurement height, while the Law‐of‐the‐Wall yields a single boundary layer estimate based on fitting a logarithmic velocity profile through the array data. Analysis reveals significant inconsistencies between estimates derived from the two methods, on both a whole‐event basis and as time‐series. Despite a near‐perfect fit of the Law‐of‐the‐Wall, the point estimates of Reynolds shear stress vary greatly between heights, calling into question the assumed presence of a constant stress layer. A comparison with simultaneously measured sediment transport finds no relationship between transport activity and the discrepancies in shear stress estimates. Results do show, however, that Reynolds shear stress measured nearer the bed exhibits slightly better correlation with sand transport rate. The findings serve as a major cautionary message to the interpretation and application of single‐height measurements of Reynolds shear stress and their equivalence to Law‐of‐the‐Wall derived estimates, and these concerns apply widely to boundary layer flows in general. © 2015 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Velocity distribution in a gradually accelerating free surface flow

This study investigates the interaction of the vertical velocity v and the streamwise velocity u in a gradually accelerating flow. The analytical result shows that the momentum of uv driven by the mean velocities in a non-uniform flow is not negligible. This additional momentum directly results in the concave profiles of Reynolds shear stress in gradually accelerating flows, a departure from the expected linear profile. Consequently, this momentum causes the maximum velocity to be located below the free surface, i.e., the dip-phenomenon. This paper investigated the interactions of the Reynolds shear stress, non-zero vertical velocity and dip-phenomenon, it is found that the non-zero vertical velocity causes the dip-phenomenon. The approach is tested using the experimental data of Song and others, and good agreements between the predicted and measured velocity profiles have been achieved.     

Velocity profiles and bed shear stress over various bed configurations in a river bend

Vertical velocity profiles measured over various bed configurations (plane beds, ripples, and dunes) in. the meandering River South Esk, Glen Clova, Scotland are presented on semilogarithmic paper. Local bed shear stress and roughness height are calculated from the lowermost parts of the profiles using the Karman-Prandtl law of the wall; these parameters, and the geometrical properties of the profiles, are related to the various bed configurations. A graphical model is used to identify profiles developed on specific regions of dune geometry, in order to discriminate those profiles that define bed shear effective in transporting sediment over dunes. An assessment is made of the errors involved in estimating local mean velocity from extrapolating the law of the wall to the water surface. A Darcy-Weisbach friction coefficient is related to bed configuration and local stream power.     

Simulation of the effect of wind speedup in the formation of transverse dune fields

A computer simulation model for transverse‐dune‐field dynamics, corresponding to a uni‐directional wind regime, is developed. In a previous formulation, two distinct problems were found regarding the cross‐sectional dune shape, namely the erosion in the lee of dunes and the steepness of the windward slopes. The first problem is solved by introducing no erosion in shadow zones. The second issue is overcome by introducing a wind speedup (shear velocity increase) factor, which can be accounted for by adding a term to the original transport length, which is proportional to the surface height. By incorporating these features we are able to model dunes whose individual shape and collective patterns are similar to those observed in nature. Moreover we show how the introduction of a non‐linear shear‐velocity‐increase term leads to the reduction of dune height, and this may result in an equilibrium dune field configuration. This is thought to be because the non‐linear increase of the transport length makes the sand trapping efficiency lower than unity, even for higher dunes, so that the incoming and the outgoing sand flux are in balance. To fully describe the inter‐dune morphology more precise dynamics in the lee of the dune must be incorporated. Copyright © 2000 John Wiley & Sons, Ltd.     

The effect of turbulent flow structures on saltation sand transport in the atmospheric boundary layer

The effect of turbulent flow structures on saltation sand transport was studied during two convective storms in Niger, West Africa. Continuous, synchronous measurements of saltation fluxes and turbulent velocity fluctuations were made with a sampling frequency of 1 Hz. The shear stress production was determined from the vertical and streamwise velocity fluctuations. The greatest stress-bearing events were classified as turbulent structures, with sweep, ejection, inward interaction, and outward interaction described according to the quadrant technique. The classified turbulent structures accounted for 63·5 per cent of the average shear stress during the first storm, and 56·0 per cent during the second storm. The percentage of active time was only 20·6 per cent and 15·8 per cent, respectively. High saltation fluxes were associated with sweeps and outward interactions. These two structures contribute positively (sweeps) and negatively (outward interactions) to the shear stress, but have in common that the streamwise velocity component is higher than average. Therefore, the horizontal drag force seems primarily responsible for saltation sand transport, and not the shear stress. This was also reflected by the low correlation coefficients (r) between shear stress and saltation flux (0·12 and 0·14, respectively), while the correlation coefficients between the streamwise velocity component and saltation flux were much higher (0·65 and 0·57, respectively). © 1998 John Wiley & Sons, Ltd.