Effect of water depth and the bottom boundary layer upon internal wave generation over abrupt topography

The role of water depth and bottom boundary layer turbulence upon lee-wave generation in sill regions is examined. Their effect upon vertical mixing is also considered. Calculations are performed using a non-hydrostatic model in cross-section form with a specified tidal forcing. Initial calculations in deeper water and a sill height such that the sill top is well removed from the surrounding bed region showed that downstream lee-wave generation and associated mixing increased as bottom friction coefficient k increased. This was associated with an increase in current shear across the sill. However, for a given k, increasing vertical eddy viscosity A _v reduced vertical shear in the across sill velocity, leading to a reduction in lee-wave amplitude and associated mixing. Subsequent calculations using shallower water showed that for a given k and A _v, lee-wave generation was reduced due to the shallower water depth and changes in the bottom boundary layer. However, in this case (unlike in the deepwater case), there is an appreciable bottom current. This gives rise to bottom mixing which in shallow water extends to mid-depth and enhances the mid-water mixing that is found on the lee side of the sill. Final calculations with deeper water but small sill height showed that lee waves could propagate over the sill, thereby reducing their contribution to mixing. In this case, bottom mixing was the major source of mixing which was mainly confined to the near bed region, with little mid-water mixing.     

Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.     

The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.     

Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions

A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear terms in the energy flux become increasingly important as the sill Froude Number (F _s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee wave generation and the non-linear contribution to the energy flux. Calculations show that as F _s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions.     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

Tidal mixing in sill regions: influence of sill depth and aspect ratio

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h _s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F _r as the sill depth (h _s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U _s due to increased depth. Calculations show that the sill Froude number F _s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F _s (namely F _s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F _s, calculations with a narrow sill show that for a given F _s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U _s show that for small values of h _s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h _s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h _s, “internal mixing” dominates the solution and controls across thermocline mixing.     

Numerical modelling of stratified tidal flow over a fjord sill

Field observations of tidally driven stratified flow in the sill area of Knight Inlet (British Columbia) revealed a very complicated structure, which includes solitary waves, upstream bifurcation, hydraulic jump and mixing processes. Recent observations suggest that the flow instabilities on the plunging pycnocline at the lee side of the sill may contribute to solitary wave generation through a subharmonic interaction. The present study reports on a series of numerical experiments of stratified tidal flow in Knight Inlet performed with the help of a fine resolution fully non-linear non-hydrostatic numerical model. The model reproduces all important stages of the baroclinic tidal dynamics observed in Knight Inlet. Results demonstrate that solitary waves are generated apart from the area of hydrodynamic instability. Accelerating tidal flux forms a baroclinic hydraulic jump just above the top of the sill, whereas the bifurcations and zones of shear instabilities are formed downstream of the sill. The first baroclinic mode having the largest velocity escapes from the generation area and propagates upstream, disintegrating further into a packet of solitary waves reviling the classical “non-subharmonic” mechanism of generation. The remaining part of the disturbance (slow baroclinic modes) is arrested by tidal flow and carried away to the lee side of the obstacle, where shear instability, billows and mixing processes are developed. Some sensitivity runs were performed for different value of tidal velocity.     

Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size

A non-hydrostatic terrain-following model in cross sectional form is applied to study the processes in the lee of a sill in an idealized stratified fjord during super-critical tidal inflow. A sequence of numerical studies with horizontal grid sizes in the range from 100 to 1.5625 m are performed. All experiments are repeated using both hydrostatic and non-hydrostatic versions of the model, allowing a systematic study of possible non-hydrostatic pressure effects and also of the sensitivity of these effects to the horizontal grid size. The length scales and periods of the internal waves in the lee of the sill are gradually reduced and the amplitudes of these waves are increased as the grid size is reduced from 100 down to 12.5 m. With a further reduction in grid size, more short time and space scale motions become superimposed on the internal waves. Associated with the internal wave activity, there is a deeper separation point that is fairly robust to all parameters investigated. Another separation point nearer to the top of the sill appears in the numerical results from the high-resolution studies with the non-hydrostatic model. Associated with this shallower separation point, an overturning vortex appears in the same set of numerical solutions. This vortex grows in strength with reduced grid size in the non-hydrostatic experiments. The effects of the non-hydrostatic pressure on the velocity and temperature fields grow with reduced grid size. In the experiments with horizontal grid sizes equal to 100 or 50 m, the non-hydrostatic pressure effects are small. For smaller grid sizes, the time mean velocity and temperature fields are also clearly affected by the non-hydrostatic pressure adjustments.     

A non-hydrostatic numerical model for calculating free-surface stratified flows

A three-dimensional non-hydrostatic numerical model for simulation of the free-surface stratified flows is presented. The model is a non-hydrostatic extension of free-surface primitive equation model with a general vertical coordinate and horizontal orthogonal curvilinear coordinates. The model equations are integrated with mode-splitting technique and decomposition of pressure and velocity fields on hydrostatic and non-hydrostatic components. The model was tested against laboratory experiments on the steep wave transformation over the longshore bar, solitary wave impact on the vertical wall, the collapse of the mixed region in the thin pycnocline, mixing in the lock-exchange flows and water exchange through the sea strait. The agreement is generally fair.Responsible Editor: Hans Burchard     

Modelling the influence of small-scale effects upon the larger scale: an oceanographic challenge

The problem of resolving or parameterising small-scale processes in oceanographic models and the extent to which small-scale effects influence the large scale are briefly discussed and illustrated for a number of cases. For tides and surges in near-shore regions, the advantages of using a graded mesh to resolve coastal and estuarine small-scale features are demonstrated in terms of a west coast of Britain unstructured mesh model. The effect of mesh resolution upon the accuracy of the overall solution is illustrated in terms of a finite element model of the Irish Sea and Mersey estuary. For baroclinic motion at high Froude number, the effect of resolving small-scale topography within a non-hydrostatic model is illustrated in terms of tidally induced mixing at a single sill, or two closely spaced sills. The question of how to parameterise small-scale non-linear interaction processes that lead to significant mixing, in a form suitable for coarser grid hydrostatic models, is briefly considered. In addition, the importance of topographically induced mixing that occurs in the oceanic lateral boundary layer, namely, the shelf edge upon the large-scale ocean circulation is discussed together with the implications for coarse grid oceanic climate models. The use of unstructured grids in these models to enhance resolution in shelf-edge regions in a similar manner to that used in storm surge models to enhance near coastal resolution is suggested as a suitable “way forward” in large-scale ocean circulation modelling.     

A semi-implicit three-dimensional numerical model for non-hydrostatic pressure free-surface flows on an unstructured,sigma grid

A semi-implicit 3-D numerical formulation for solving non-hydrostatic pressure free-surface flows on an unstructured,sigma grid is proposed.Pressure-splitting and 9 semi-implicit methods are inherited and reformed from Casulli’s z-coordinate formulation.The non-orthogonal sigma-coordinate transformation leads to additional terms. The resulting linear system for the non-hydrostatic correction is diagonally dominant but unsymmetric,and it is solved by the BiCGstab method.In contrast with z-coordinate non-hydrostatic models,the new model fits vertical boundaries much better,which is important for the long-time simulation of sediment transport and riverbed deformation.A lock-exchange density flow is computed to determine whether the new scheme is able to simulate non-hydrostatic free-surface flows.The new model is further verified using the field data of a natural river bend of the lower Yangtze River.Good agreement between simulations and earlier research results,field data is obtained, indicating that the new model is applicable to hydraulic projects in real rivers.     

Lateral circulation driven by boundary mixing and the associated transport of sediments in idealized partially mixed estuaries

A three-dimensional, hydrostatic, primitive equation numerical model with modern turbulence closures is used to explore lateral circulation and the associated transport of sediments in idealized, moderately to highly stratified estuaries. The model results suggest that boundary mixing on a sloping bottom can drive a significant amount of lateral circulation. This mechanism has received little attention to date in the estuarine literature. Good agreement with an analytical solution and similar vertical structures of lateral flows to observations from the Hudson River estuary support the importance of the boundary mixing mechanism. Boundary mixing is at least as important as differential advection for the modeled scenarios, when the two mechanisms are evaluated using the salt balance equation for model runs without rotation. Linearly superposing analytical solutions for lagged boundary mixing lateral flow and Ekman-forced lateral flow yields a good representation of the near-bottom lateral flow from the model with rotation. The 2 h lag required for the boundary mixing solution is roughly equal to the vertical diffusion time scale, indicating that lateral flow adjustment depends on development of a bottom mixed layer. Sediment dynamics at cross sections seaward and landward of the salt intrusion are very different. Seaward of the salt intrusion, sediments are eroded in the channel and preferentially deposited on the right slope (looking seaward), mainly due to the combination of high sediment concentration in the channel during flood with strong up-slope transport on that side (tidal pumping). Lateral sediment re-distribution landward of the salt intrusion is negligible due to weak residual lateral circulation.     

Analytical modelling of wintertime coastal jets in the Adriatic Sea

Two diagnostic models, reproducing circulation generated in a marginal sea by variable density, have been developed. The models’ domain is a 2D transverse section for which analytical solutions have been obtained. They describe the winter situation in the northern Adriatic, with a strong vertical mixing present and the density maximum dominating the centre of the basin. Both models employ Boussinesq-type parametrisation of friction and linear slip at the bottom. The first model allows for frictional departure from hydrostatic equilibrium and includes vertical friction only. The second one is hydrostatic but allows for lateral friction as well. The results obtained by the two models are similar and to some extent dependent on the vertical and bottom friction. They reproduce several well known characteristics of the Adriatic circulation (cyclonic surface flow, downwelling in the central and larger part of the basin compensated by upwelling in the coastal zone) but also predict some phenomena that are still not well understood. A conspicuous feature of the model results are coastal jets, which were observed in the Adriatic on several occasions. The present models show that the distance of jets from the coasts depends on lateral friction: it is found to vary from 1 up to 10 km on the Italian side and between 2 and 15 km on the Croatian side. Both models reproduce the west–east asymmetry, with the wider current on the east side of the basin. The asymmetry is a subject on which conflicting empirical results exist in the Adriatic. In the two models cyclonic flow occupies the whole water column, which disagrees with some recent theoretical findings of the near-bottom anticyclonic flow and thus leaves the issue open.     

Three‐dimensional flow structure around small‐scale bedforms in a simulated gravel‐bed environment

Pebble clusters are common small‐scale morphological features in gravel‐bed rivers, occupying as much as 10 per cent of the bed surface. Important links exist between the presence of pebble clusters and the development of flow structures. These links are poorly understood at the three‐dimensional level. Particularly neglected has been the effect of clusters on the lateral flow characteristics. A laboratory study was conducted using a hydraulic flume, within which simulated pebble clusters were superimposed onto a plane bed of gravel material. High‐resolution three‐dimensional flow data were collected above the bed at two different flow depths using an acoustic Doppler velocimeter. The results present evidence of the importance of lateral flow in the development of turbulent flow structure. Narrow regions of high lateral and downstream turbulence intensity exist to both sides of clusters and in a three‐dimensional separation zone in their lee. This may indicate the presence of horseshoe‐type vortical structures analogous to those identified in less hydraulically rough environments. However, it is likely that these structures are more complicated given the mutual interference of the surrounding medium. The lateral flow was also identified as a key component in the upwelling identified by other authors in the lee of pebble clusters. The results of the vertical flow analysis confirm the hypothesis that six regions with distinct vertical flow characteristics exist above clusters: flow acceleration up the stoss‐side of the cluster; recirculation behind the cluster in the wake region; vortex shedding from the pebble crest and shear layer; flow reattachment downstream of the cluster; upwelling of flow downstream of the point of reattachment; and recovery of flow. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions

A non-linear two-dimensional vertically stratified cross-sectional model of a constant depth basin without rotation is used to investigate the influence of vertical and horizontal diffusion upon the wind-driven circulation in the basin and the associated temperature field. The influence of horizontal grid resolution, in particular the application of an irregular grid with high resolution in the coastal boundary layer is examined. The calculations show that the initial response to a wind impulse is downwelling at the downwind end of the basin with upwelling and convective mixing at the opposite end. Results from a two-layer analytical model show that the initial response is the excitation of an infinite number of internal seiche modes in order to represent the initial response which is confined to a narrow near coastal region. As time progresses, at the downwind end of the basin a density front propagates away from the boundary, with the intensity of its horizontal gradient and associated vertical velocity determined by both horizontal and vertical viscosity values. Calculations demonstrate the importance of high horizontal grid resolution in resolving this density gradient together with an accurate density advection scheme. The application of an irregular grid in the horizontal with high grid resolution in the nearshore region enables the initial response to be accurately reproduced although physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. Parameterization of horizontal viscosity using a Smagorinsky-type formulation acts as a selective grid size-dependent filter, and removes the short-wave problem although enhanced smoothing can occur if the scaling coefficient in the formulation is too large. Calculations clearly show the advantages of using an irregular grid but also the importance of using a grid size-dependent filter to avoid numerical problems.     

A model study of spin-down and circulation in a cold water dome

A three-dimensional prognostic hydrodynamic model in cross sectional form is used to examine the influence of bottom friction, mixing and topography upon the spin-down and steady-state circulation in a cold water bottom-dome. Parameters characteristic of the Irish Sea or Yellow Sea cold water domes are used. In all calculations, motion is induced by specifying an initial temperature distribution characteristic of the dome, and an associated along frontal flow. The spin-down of the dome is found to be influenced by the coefficient of bottom friction, with a typical time scale of order 10 days, and in general to be independent of the chosen initial vertical profile of along frontal flow. However, in the case in which the along frontal flow is such that the near bed velocity is zero, then bottom stress is also zero, and there is no appreciable spin-down. Calculations showed that the formulation of viscosity and diffusivity had a greater effect upon the steady-state circulation than topography, suggesting that background mixing of tidal origin is important. The lack of topographic influence was due mainly to the formulation of the initial conditions which were taken to be independent of topography. The steady-state circulation was characterized by a cyclonic flow in the surface region, with an anti-cyclonic current near the bed, where frictional effects produced a bottom Ekman layer and an across frontal flow. This gave rise to vertical circulation cells in the frontal region of the dome with prevailing downwelling motion inside the dome. A detailed analysis of the dynamic balance of the various terms in the hydrodynamic equations yielded insight into the processes controlling the steady-state circulation in cold water domes. Responsible Editor: Phil Dyke     

Lateral variability of flow over a sill in a channel of southern Chile

Measurements of velocity and density profiles were used to describe the tidal and mean flow structure across and along a sill in Refugio Channel, a fjord-like inlet in Southern Chile (43.9°S). These are the first oceanographic measurements of any kind effected in Refugio Channel. Current profiles were obtained with a 307.2-kHz acoustic Doppler current profiler during two semidiurnal cycles along a repeated triangular circuit. Two along-channel transects formed the sides of the triangle that crossed the sill and were identified as the western and eastern transects. One cross-channel transect, the base of the triangle, was located on the seaward side of the sill. Density profiles were obtained at the corners of the triangle. The longitudinal mean flow in the western transect showed a two-layer exchange structure over the landward side of the sill. The structure of net seaward flow at the surface and landward flow at depth was disrupted by the sill in such a way that over the seaward side of the sill, only seaward flow was observed throughout the water column. This likely resulted from the blocking of landward net flow by the sill. In the eastern transect, two-layer exchange dominated over most of the transect and was consistent with the observed density profiles. Over the seaward side of the sill, a surface layer, ∼10m deep, flowed landward as a third layer. This feature should have been caused by river input further seaward (to the north) and produced a surface convergence region over the sill. In terms of tidal flows, the greatest tidal current amplitudes were 40cm s⁻¹ over the sill as the flow accelerated through the reduced cross-sectional area of the channel. Near-surface flow convergences were identified over both along-channel transects.     

Influence of open boundary conditions and sill height upon seiche motion in a gulf

A cross-sectional model of an idealised constant depth gulf with a sill at its entrance, connected to a deep ocean, is used to examine the barotropic and baroclinic response of the region to wind forcing. The role of the oceanic boundary condition is also considered. Calculations show that in the case of a tall sill, where the pycnocline intersects the sill, the baroclinic response of the gulf is similar to that of a lake, and internal waves cannot radiate energy out of the gulf. The barotropic response shows free surface oscillations, with nodes located close to the centre of the oceanic basin and entrance to the gulf, with associated barotropic resonant periods. As the sill height is reduced, baroclinic wave energy is radiated from the gulf into the ocean, and the form of the baroclinic response changes from a standing wave (tall sill) as in a lake to a progressive wave (no sill). The location of sea surface elevation nodes and resonant periods changes as the sill height is reduced. Calculations of the barotropic resonant periods with and without stratification could not determine if they were influenced by the presence of stratification, although published analytical theory suggests that they should be able to when energy is lost from the gulf by internal wave radiation. This inability to detect changes in barotropic resonant period due to stratification effects is due to the small change in resonant frequency produced by baroclinic effects, as shown by analytical results, and the broad peak nature of the computed resonant frequency. In the case of a closed offshore boundary (an offshore island), there is a stronger and narrower energy peak at the resonant frequency than when a barotropic radiation condition is applied. However, the influence of stratification upon the resonant frequency could not be accurately determined. Although the offshore boundary was well removed from the gulf to such an extent that any baroclinic waves reflected from it could not reach the gulf within the integration period, it did, however, slightly influence the gulf baroclinic response due to its influence on the barotropic response.     

Deep circulation driven by strong vertical mixing in the Timor Basin

The importance of deep mixing in driving the deep part of the overturning circulation has been a long debated question at the global scale. Our observations provide an illustration of this process at the Timor Basin scale of ～1000 km. Long-term averaged moored velocity data at the Timor western sill suggest that a deep circulation is present in the Timor Basin. An inflow transport of ～0.15 Sv is observed between 1600 m and the bottom at 1890 m. Since the basin is closed on its eastern side below 1250 m depth, a return flow must be generated above 1600 m with a ～0.15 Sv outflow. The vertical turbulent diffusivity is inferred from a heat and transport balance at the basin scale and from Thorpe scale analysis. Basin averaged vertical diffusivity is as large as 1 × 10^?3 m² s^?1. Observations are compared with regional low-resolution numerical simulations, and the deep observed circulation is only recovered when a strong vertical diffusivity resulting from the parameterization of internal tidal mixing is considered. Furthermore, the deep vertical mixing appears to be strongly dependent on the choice of the internal tide mixing parameterization and also on the prescribed value of the mixing efficiency.     

Suspended sediment transport and deposition over a dune: Río Paraná, Argentina

Field data from the Rio Paraná, Argentina, are used to examine patterns of suspended sediment transport over a sand dune. Measurements of three‐dimensional velocity are made with an acoustic Doppler current profiler whilst suspended sediment concentration and particle size have been quantified using a laser in situ sediment scattering transmissometer. Suspended sediment concentration and streamwise and vertical sediment flux are highest close to the bed, with an upward vertical flux over the stoss side of the dune and downward flux over the lee side. Suspended sediment concentrations are higher over the crest compared with the trough and suspended sediment is coarsest near the bed. About 17% of the suspended‐load transported over the crest is deposited in the lee side before it reaches the trough. Most of this deposited sand is coarser sediment that originates close to the bed over the crest, a result consistent with simulations based on the model of Mohrig and Smith (Water Resources Research 1996; 32: 3207–3217) for the excursion lengths of sediment dispersed in the lee side of a dune. Copyright © 2009 John Wiley & Sons, Ltd.