Direct numerical simulation of low Reynolds number oscillating boundary layers on adiabatic slopes

TL;DR

This study uses direct numerical simulation to analyze the stability and transition to turbulence of stratified boundary layers on slopes under oscillatory forcing, relevant to oceanic internal tides, revealing conditions that stabilize or sustain turbulence.

Contribution

It provides new insights into the mechanisms of instability and turbulence in stratified boundary layers on slopes under oscillatory conditions, especially regarding the effects of stratification and rotation.

Findings

Boundary layers are stabilized by increased stratification during downslope oscillation.

Turbulence is sustained throughout oscillation when rotation effects are significant.

Oscillating boundary layers from low wavenumber tides do not cause significant irreversible mixing.

Abstract

We investigate the instabilities and transition mechanisms of Boussinesq stratified boundary layers on sloping boundaries when subjected to oscillatory body forcing parallel to the slope. Such conditions are typical of the boundary layers generated by low wavenumber internal tides sloshing up and down adiabatic abyssal slopes in the absence of mean flows, high wavenumber internal tides, and resonant tide-bathymetry interactions. We examine flows within a region of non-dimensional parameter space typical of the mid- to low-latitude oceanic $M_2$ tides on hydraulically smooth abyssal slopes by direct numerical simulation. We find that at low Reynolds numbers transition-to-turbulence pathways arise from both shear and gravitational instabilities, and we find that the boundary layers are stabilized by increased outer boundary layer stratification during the downslope oscillation phase. However, if rotation is significant (low slope Burger numbers) we find that boundary layer turbulence is sustained throughout the oscillation period, resembling Stokes-Ekman layer turbulence. Our results suggest that oscillating boundary layers on smooth abyssal slopes created by low wavenumber $M_2$ tides do not cause significant irreversible turbulent buoyancy flux (mixing) and that flat-bottom dissipation rate models derived from the tide amplitude are accurate within an order of magnitude.