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Subaqueous vortex ripples in equilibrium are characterized by their unique geometry and dimensions. Motivated by the recent direct numerical simulation study of oscillatory turbulent flow over a wavy bottom by Önder & Yuan ( J. Fluid Mech. , vol. 858, 2019, pp. 264–314), the objective of this study is to further investigate the fluid dynamical controls that determine the distinctive equilibrium dimensions of vortex ripples. We use direct numerical simulations to investigate the differences in flow kinetics between sinusoidal oscillatory flow over equilibrium and out-of-equilibrium vortex ripples. In comparison with the equilibrium case, the spanwise coherent vortices, the averaged bottom shear stress on overlying flow and the shear stress distribution on the ripple surface are identified as the key fluid dynamical controls on equilibrium dimensions. Based on these controls, we propose mechanisms in the selection of vortex ripple dimensions. We observe that the flow adjusts in such a way that the interaction between overlying flow and vortex ripples tends to generate the strongest coherent vortices while the ripple surface (or overlying flow) experiences the smallest shear stress averaged over ripple wavelength during the selection process. Through a triple decomposition of the flow, the component of the ripple-induced fluctuation is found to dictate these fluid dynamical controls, which implies that this component plays an important role in the evolution of vortex ripples. 

Abstract Wave‐ and current‐supported turbidity currents (WCSTCs) are one of the sediment delivery mechanisms from the inner shelf to the shelf break. Therefore, they play a significant role in the global cycles of geo‐chemically important particulate matter. Recent observations suggest that WCSTCs can transform into self‐driven turbidity currents close to the continental margin. However, little is known regarding the critical conditions that grow self‐driven turbidity currents out of WCSTCs. This is in part due to the knowledge gaps in the dynamics of WCSTCs regarding the role of density stratification. Especially the effect of sediment entrainment on the amount of sediment suspension has been overlooked. To this end, this study revisits the existing theoretical framework for a simplified WCSTC, in which waves are absent, that is, along‐shelf current‐supported turbidity current. A depth‐integrated advection model is developed for suspended sediment concentration. The model results, which are verified by turbulence‐resolving simulations, indicate that the amount of suspended sediment load is regulated by the equilibrium among positive/negative feedback between entrainment and cross‐shelf gravity force/density stratification, and settling flux dissociated with density stratification. It is also found that critical density stratification is not a necessary condition for equilibrium. A quantitative relation is developed for the critical conditions for self‐driven turbidity currents, which is a function of bed shear stress, entrainment parameters, bed slope, and sediment settling velocity. In addition, the suspended sediment load is analytically estimated from the model developed.