The interactions between turbulence events and sediment motions during bed load transport were studied by means of laser-Doppler velocimetry and high-speed cinematography. Sweeps (u′ > 0, w′ 0 w′ > 0) which contribute negatively to the bed shear stress and are relatively rare, individually move as much sediment as sweeps of comparable magnitude and duration, however, and much more than bursts (u′ 0) and inward interactions (u′ < 0, w′ < 0). When the magnitude of the outward interactions increases relative to the other events, therefore, the sediment flux increases even though the bed shear stress decreases. Thus, although bed shear stress can be used to estimate bed load transport by flows with well-developed boundary layers, in which the flow is steady and uniform and the turbulence statistics all scale with the shear velocity, it is not accurate for flows with developing boundary layers, such as those over sufficiently nonuniform topography or roughness, in which significant spatial variations in the magnitudes and durations of the sweeps, bursts, outward interactions, and inward interactions occur. These variations produce significant peaks in bed load transport downstream of separation points, thus supporting the hypothesis that flow separation plays a significant role in the development of bed forms.

Role of Near-Bed Turbulence Structure in Bed Load Transport and Bed Form Mechanics

[1] Dunes are present in nearly all fluvial channels and are vital in predicting flow resistance, sediment transport, and deposition within many rivers. Progress in understanding the fluid dynamics associated with alluvial dunes has been significant in the last 15 years and has witnessed huge advances in field, laboratory, and numerical investigations. Progress has been made in detailing the principal features of mean and turbulent flow over asymmetric dunes that possess flow separation in their leesides and how these forms affect both downstream boundary layer structure and stress partitioning over the dune. Additionally, the links between sediment transport over dunes and instantaneous coherent flow structures are being increasingly understood, with the feedback of dune three-dimensionality upon flow and sediment dynamics over these bed forms beginning to be recognized as vital. Such research now provides an outstanding background for beginning to address areas of greater complexity that will enable a fuller understanding of these important natural features. This review paper summarizes the principal features of mean and turbulent flow over alluvial sand dunes. Five areas are then highlighted and discussed as a possible focus for future research: (1) the influence of dune leeside angle upon flow processes in the dune wake and downstream flow field, (2) the influence of three-dimensionality in dune shape upon the generation of turbulence and distribution of bed shear stress, (3) flow field modification resulting from bed form superimposition and amalgamation, (4) the scale and topology of dune-related turbulence and its interactions with sediment transport and the flow surface, and (5) the influence of suspended sediment on the dune flow field and dune morphology.

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The fluid dynamics of river dunes: A review and some future research directions

[1] Dunes are present in nearly all fluvial channels and are vital in predicting flow resistance, sediment transport, and deposition within many rivers. Progress in understanding the fluid dynamics associated with alluvial dunes has been significant in the last 15 years and has witnessed huge advances in field, laboratory, and numerical investigations. Progress has been made in detailing the principal features of mean and turbulent flow over asymmetric dunes that possess flow separation in their leesides and how these forms affect both downstream boundary layer structure and stress partitioning over the dune. Additionally, the links between sediment transport over dunes and instantaneous coherent flow structures are being increasingly understood, with the feedback of dune three-dimensionality upon flow and sediment dynamics over these bed forms beginning to be recognized as vital. Such research now provides an outstanding background for beginning to address areas of greater complexity that will enable a fuller understanding of these important natural features. This review paper summarizes the principal features of mean and turbulent flow over alluvial sand dunes. Five areas are then highlighted and discussed as a possible focus for future research: (1) the influence of dune leeside angle upon flow processes in the dune wake and downstream flow field, (2) the influence of three-dimensionality in dune shape upon the generation of turbulence and distribution of bed shear stress, (3) flow field modification resulting from bed form superimposition and amalgamation, (4) the scale and topology of dune-related turbulence and its interactions with sediment transport and the flow surface, and (5) the influence of suspended sediment on the dune flow field and dune morphology.

The fluid dynamics of river dunes : A review and some future research directions : Marine sandware and river dune dynamics

Detailed measurements of flow velocity and its turbulent fluctuation were obtained over fixed, two-dimensional dunes in a laboratory channel. Laser Doppler anemometry was used to measure the downstream and vertical components of velocity at more than 1800 points over one dune wavelength. The density of the sampling grid allowed construction of a unique set of contour maps for all mean flow and turbulence parameters, which are assessed using higher moment measures and quadrant analysis. These flow field maps illustrate that: (1) the time-averaged downstream and vertical velocities agree well with previous studies of quasi-equilibrium flow over fixed and mobile bedforms and show a remarkable symmetry from crest to crest; (2) the maximum root-mean-square (RMS) of the downstream velocity values occur at and just downstream of flow reattachment and within the flow separation cell; (3) the maximum vertical RMS values occur within and above the zone of flow separation along the shear layer and this zone advects and diffuses downstream, extending almost to the next crest; (4) positive downstream skewness values occur within the separation cell, whereas positive vertical skewness values are restricted to the shear layer; (5) the highest Reynolds stresses are located within the zone of flow separation and along the shear layer; (6) high-magnitude, high-frequency quadrant-2 events (‘ejections’) are concentrated along the shear layer (Kelvin-Helmholtz instabilities) and dominate the contribution to the local Reynolds stress; and (7) high-magnitude, high-frequency quadrant-4 events occur bounding the separation zone, near reattachment and close to the dune crest, and are significant contributors to the local Reynolds stress at each location. These data demonstrate that the turbulence structure associated with dunes is controlled intrinsically by the formation, magnitude and downstream extent of the flow separation zone and resultant shear layer. Furthermore, the origin of dune-related macroturbulence lies in the dynamics of the shear layer rather than classical turbulent boundary layer bursting. The fluid dynamic distinction between dunes and ripples is reasoned to be linked to the velocity differential across the shear layer and hence the magnitude of the Kelvin-Helmholtz instabilities, which are both greater for dunes than ripples. These instabilities control the local flow and turbulence structure and dictate the modes of sediment entrainment and their transport rates.

Mean flow and turbulence structure over fixed, two-dimensional dunes: implications for sediment transport and bedform stability

The goal of this paper is to discuss the spatial averaging concept in environmental hydraulics and develop it further by considering transport equations for fluid momentum, passive substances, and suspended sediments. The averaging theorems, the double-averaged (in time and in space) fluid momentum equation, and advection-diffusion equations for a passive substance and suspended sediments are introduced and their limitations and applications for modeling rough-bed flows, experimental design, and data interpretation are discussed. The suggested equations differ from those considered in terrestrial canopy aerodynamics and porous media hydrodynamics by accounting for roughness mobility, change in roughness density in space and time, and particle settling effects for the case of suspended sediments. We show that the form of the double-averaged equations may depend on the type of decomposition of flow variables and that this difference may have important implications for modeling. We also show that the suggested methodology offers better definitions for hydraulic characteristics, variables, and parameters such as flow uniformity, flow two dimensionality, and bed shear stress.

Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: Theoretical Background

Turbulence measurements from the flow over two-dimensional fixed dune shapes are presented along with analysis and discussion of the ramifications of the observations for transport of sediment as bed load over bed forms The spatial structure of the local transport rate determines the shape and stability of bed forms such as ripples and dunes, and the transport of sediment is a highly nonlinear process that is profoundly affected by the statistics of the temporal fluctuations in the near-bed flow field The measurements presented herein show strong spatial evolution of the joint probability distribution of the streamwise and bednormal fluctuating velocity components Unlike measurements in uniform boundary layers, these distributions and the higher moments of the velocity do not scale with the local shear velocity, indicating that it is probably inappropriate to use the shear stress to characterize the sediment flux This conclusion is supported by observations of sediment flux over a dune

Turbulence structure over two‐dimensional bed forms: Implications for sediment transport

Vertical profiles of streamwise velocity measured over bed forms are commonly used to deduce boundary shear stress for the purpose of estimating sediment transport. These profiles may be derived locally or from some sort of spatial average. Arguments for using the latter procedure are based on the assumption that spatial averaging of the momentum equation effectively removes local accelerations from the problem. Using analogies based on steady, uniform flows, it has been argued that the spatially averaged velocity profiles are approximately logarithmic and can be used to infer values of boundary shear stress. This technique of using logarithmic profiles is investigated using detailed laboratory measurements of flow structure and boundary shear stress over fixed two-dimensional bed forms. Spatial averages over the length of the bed form of mean velocity measurements at constant distances from the mean bed elevation yield vertical profiles that are highly logarithmic even though the effect of the bottom topography is observed throughout the water column. However, logarithmic fits of these averaged profiles do not yield accurate estimates of the measured total boundary shear stress.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JC900116

Spatially averaged flow over a wavy boundary revisited

To estimate bed-load sediment transport rates in flows over bed forms such as ripples and dunes, spatially averaged velocity profiles are frequently used to predict mean boundary shear stress. However, such averaging obscures the complex, nonlinear interaction of wake decay, boundary-layer development, and topographically induced acceleration downstream of flow separation and often leads to inaccurate estimates of boundary stress, particularly skin friction, which is critically important in predicting skin friction over 2D bed forms. The approach is based on combining the equations describing the mechanics of the internal boundary layer with semi-empirical structure functions to predict the velocity at the crest of a bed form, where the flow is most similar to a uniform boundary layer. Significantly, the methodology is directed toward making specific predictions only at the bed-form crest, and as a result it avoids the difficulty and questionable validity of spatial averaging. The model provides an accurate estimate of the skin friction at the crest where transport rates are highest. Simple geometric constraints can be used to derive the mean transport rates as long as bedload is dominant.

S. R. Wolfe

Papers

Turbulence structure over two‐dimensional bed forms: Implications for sediment transport

Spatially averaged flow over a wavy boundary revisited

Predicting Boundary Shear Stress and Sediment Transport over Bed Forms