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 manuscript 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 (MIM) 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, θML, obtained by depth-averaging across the mobile layer of grains, is shown to be approximately one-half the magnitude of the Shields parameter at the top of the mobile layer, and, as is illustrated in the companion paper (DeVoe et al., Manuscript submitted for review), 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.

Volumetric bedload transport and the thickness of the mobile layer of sediment grains are examined using data from a high-resolution, two-phase numerical simulation of oscillatory flow over an erodible, rippled bed. The spatiotemporal distribution of mobile layer thickness and the spatially-averaged bedload flux exhibit a similar dual-peak behavior to the depth-averaged mobile layer Shields parameter, θML, which was derived in the companion paper, DeVoe et al. (Manuscript submitted for review). This supports the suggestion that θML is a better predictor of bedform motion than the Shields parameter taken on the surface of the bedform alone. Spatially-averaged estimates of θML are in excellent agreement with the Shields parameter inferred from the semi-empirical Meyer-Peter and Müller (1948) (”M-P&M”) formula, suggesting the M-P&M is suitable for estimating net bedload flux or spatially-averaged mobile layer thickness when the two-dimensional flow field over the ripple is resolved. However, we show that neither mobile layer thickness nor volumetric flux can be predicted via shear stress estimated from a singular velocity profile unless the profile is collected at the ripple crest.