Boundary streaming by internal waves

TL;DR

This paper investigates how boundary conditions affect the generation of mean flows by internal waves in stratified fluids, highlighting the importance of boundary streaming in wave-mean flow interactions.

Contribution

It provides a detailed analysis of boundary streaming effects near undulating walls emitting internal waves, emphasizing the impact of boundary conditions and boundary layers.

Findings

Boundary conditions significantly influence boundary streaming strength.

Bulk streaming dominates over boundary streaming at larger times.

Boundary layers affect flow reversals in wave-mean flow models.

Abstract

Damped internal wave beams in stratified fluids have long been known to generate strong mean flows through a mechanism analogous to acoustic streaming. While the role of viscous boundary layers in acoustic streaming has thoroughly been addressed, it remains largely unexplored in the case of internal waves. Here we compute the mean flow generated close to an undulating wall that emits internal waves in a viscous, linearly stratified two-dimensional Boussinesq fluid. Using a quasi-linear approach, we demonstrate that the form of the boundary conditions dramatically impacts the generated boundary streaming. In the no-slip scenario, the early time Reynolds stress divergence within the viscous boundary layer is much stronger than within the bulk while also driving flow in the opposite direction. Whatever the boundary condition, boundary streaming is however dominated by bulk streaming at a larger time. Using a WKB approach, we investigate the consequences of adding boundary streaming effects to an idealised model of wave-mean flow interactions known to reproduce the salient features of the quasi-biennial oscillation. The presence of wave boundary layers has a quantitative impact on the flow reversals.