Spatially averaged flow over a wavy boundary revisited (original) (raw)

1999, Journal of Geophysical Research: Oceans

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 twodimensional 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 •opography 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. 1. Introduction When acted upon by a flow that is of sufficient strength to initiate general motion of the uppermost particles, erodible beds are typically unstable. Asymmetrical bed forms such as ripples or dunes generally result when the mode of transport of these particles is primarily as bed load, wl•ere the grains slide, roll, or hop along the bed. Such bed features cause the ove, rlying flow to separate, creating a flow that is characterized by complex interactions between the flow field, the topography, and the sediment itself. The complex interdependence among flow, bed geometry, and sediment transport limits the ability of investigators to make accurate predictions of boundary shear stress, sediment-transport rates, and changes in bottom topography. Such predictions are of critical importance in certain aspects of environmental science and engineering such as design, maintenance, or restoration of channels and harbors. An important quantity of interest regarding flow over bed forms is the total drag. In rivers and flood channels, flow resistance is a key factor in predicting the stage as a function of discharge. In the marine environment, drag coefficients depend strongly on the nature of bed forms that may be present. The total drag exerted by flow over a boundary that is characterized by forms such as ripples and dunes is greater than if the boundary were flat. The increase in drag arises because of the pressure distribution over the bed forms (form drag). The pressure is lowest over the crest and separation region downstream of it and rises rapidly to its highest value in the vicinity of the reattachment region near the base of the upslope. Form drag often accounts for the majority of the total drag; therefore accurate estimates of this quantity are critical. Because the length scale that characterizes the variation in