Selection of Vortex Ripple Dimensions in Sinusoidal Oscillatory Flows

Abstract:

Subaqueous sand ripples are ubiquitous in the coastal ocean, and hence investigating turbulent oscillatory flow over ripples is vital to the understanding of hydrodynamic dissipation and sediment transport. When the near-bed wave orbital motion induced by surface gravity waves is strong enough to mobilize sand grains on the seafloor, nearly symmetrical wave ripples appear due to the redistribution of the mobilized sands. Termed by Bagnold & Taylor (1946, Proc. R. Soc. Lond. A), vortex ripples are characterized by the prominence of spanwise vortices in the overlying flow near the ripple surface (Ӧnder & Yuan 2019, J. Fluid Mech.). In addition, vortex ripples in equilibrium have ripple wavelengths of approximately 0.65 of the wave orbital diameter and ripple heights of approximately 0.17 of their wavelengths. Though this empirical understanding has been widely reported in literature (e.g. Nelson et al. 2013, J. Geophys. Res. Oceans), the formation mechanism of these topographical features on the seafloor is still not well understood. Through direct numerical simulations of sinusoidal oscillatory flow over out-of-equilibrium vortex ripples, the fluid dynamical controls of the columnar coherent vortices, the bottom shear stress on overlying flow, and the shear stress on the ripple surface are found to be important in the determination of vortex ripple dimensions. Based on the strength of the columnar coherent vortex and the shear stress on the ripple surface (or flow resistance on overlying flow), we propose a mechanism that determines vortex ripple dimensions, such that the interaction between overlying flow and vortex ripples tends to generate stronger coherent vortices while the ripple surface (or overlying flow) experiences a lesser shear stress during the process. Triple-decomposition of simulated flows shows the component of ripple-induced fluctuation is responsible for most of the fluid dynamical features contributing to the dimension selection processes. The interaction of this component with ripple-averaged wave-induced motion and turbulent fluctuation are studied through the streamwise momentum balance and vertical kinetic energy budgets. These results imply that the ripple-induced fluctuation plays a dominant role in the evolution of vortex ripples.