Turbulent flow over three-dimensional dunes: 2. Fluid and bed stresses

Dunes formed in response to fluid flow exert a total boundary stress on the fluid that is made up of form drag and skin friction, the latter of which is generally considered important for predicting sediment transport and dune evolution. Previous research has used various methods to estimate the total stress and its subcomponents, with recent work suggesting the application of a spatial average to the equations of motion. A complete, three-dimensional (3-D) form of this analysis is derived and applied to recent measurements of turbulent open-channel flow over 3-D dunes. Spatial averages of Reynolds shear stresses over 3-D dunes cannot be used to predict total boundary shear stress. However, estimations of total boundary shear stress from the spatially averaged equations of motion agree with not only the sum of form drag and skin friction but also the direct measurements of average free surface slope. Form-induced stresses from secondary circulations augment the relatively low Reynolds shear stresses over the 3-D dunes. These low turbulence levels have ramifications for sediment transport predictions, in that use of the total boundary shear stress in prediction of sediment transport over 3-D dunes must account for these low turbulence levels so as not to overpredict transport rates.