Characterization of the Spatiotemporal Distribution of Shear Stress and Bedload Flux Within a Mobile, Rippled Bed

Abstract

Mobile sediment layer dynamics and the distribution of shear stress within mobile fluid-sediment mixtures are not well understood, particularly for oscillatory flows over rippled boundaries. This article provides insight into bed shear stress at and within a mobile, rippled bedform at high spatiotemporal resolution for the purpose of improving estimates of bedload transport. Data from a coupled Large Eddy Simulation (LES) and Discrete Particle Model (DPM) is used to characterize the spatiotemporal distribution of shear stress within the bed. Estimates of stress within the mobile layer are obtained using a new momentum integral method expression for oscillatory flow over mobile, porous, non-planar boundaries that makes no a priori assumptions about the boundary layer shape. Shear stress within the mobile layer and the resulting bedload flux show a strong response to the near-bed flow. Two local maxima occur within the mobile layer shear stress distribution during each half-oscillation period that coincide with near-bed fluid acceleration and the formation of a lee-side ripple vortex. The depth-averaged mobile layer Shields parameter, ${\tilde{\theta }}_{ML}$, obtained by depth-averaging across the mobile layer of grains, is approximately one-half the magnitude of the Shields parameter at the top of the mobile layer, and may serve as a better indicator of bedform motion for rippled beds subjected to oscillatory flow. Findings highlight the implications of the assumed bed elevation on the resulting magnitude and direction of estimated shear stress, as well as discrepancies in the magnitude and phase of bedload flux estimated with existing semi-empirical formulae.