Numerical Investigation of Turbulence Modulation by Sediment-Induced Stratification and Enhanced Viscosity in Oscillatory Flows

Abstract

Recent turbulence-resolving simulations of fine sediment transport in the oscillatory bottom boundary layer (OBBL) revealed the existence of a diverse range of flow regimes over muddy seabeds. Transitions between these flow regimes are caused by different degrees of sediment-induced stable density stratification in the OBBL. These transitions have critical implications for the role of wave resuspension in the delivery of fine sediment and hydrodynamic dissipation over muddy seabeds. This study further investigates the effect of Newtonian rheology, parameterized as a concentration-dependent effective viscosity, on turbulence modulation and the transition from turbulent to laminar states. Assuming small particle Stokes number, the equilibrium approximation is adopted to simplify the Eulerian two-phase flow governing equations. The resulting simplified equations are solved with a high-accuracy hybrid scheme in an idealized OBBL. A sixth-order centered compact finite difference is implemented in the vertical direction to solve the governing equations with a flow-dependent viscosity while the pseudospectral method is retained for two horizontal directions. At Stokes Reynolds number RΔ=1,000, simulations reveal that when rheology is incorporated, the enhanced effective viscosity can further attenuate the flow turbulence in addition to the well-known sediment-induced stable density stratification. Through the enhanced viscosity, the velocity gradient very near the bed is significantly reduced, which leads to much weaker turbulent production and the onset of laminarization. Although the sediment-induced stable density stratification is known to cause laminarization of bottom boundary layer flows, our preliminary finding that the enhanced viscosity via rheological stresses encourages the flow laminarization may be useful in explaining the field-observed large wave dissipation rate over muddy seabeds during the waning stage of a storm.