Spatially averaged flow over a wavy surface

Abstract

An understanding of the mechanics of nonuniform flow is important in a variety of ecological and geophysical fluid mechanical problems. Moreover, the ability to predict local boundary shear stress on an uneven bed is essential in erosion and sediment transport problems. In order to elucidate the important fluid mechanical phenomena active over natural quasi-two-dimensional bed forms a series of detailed flow measurements were made above 60- to 100-m-long 1- to 3-m-high dunes in the Columbia River. In this paper, velocity profiles obtained by averaging these flow data along lines of constant distance above the riverbed are examined, and it is shown that they can be constructed from well-known uniform flow results used in conjunction with a hypothesis about the structure of internal boundary layers. This approach permits skin friction as well as total boundary shear stress, averaged over one wavelength of the bed form, to be determined from spatially averaged velocity profiles and, conversely, provides a mechanism whereby zero-order velocity profiles can be constructed for two-dimensional nonuniform channel flows. Corrections for changes in the bottom roughness parameter caused by bed load transport and for flow stratification induced by suspended load transport are derived and applied in order to make the results consistent with the measured spatially averaged shear stress field.