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Boundary streaming by internal waves

Published online by Cambridge University Press:  31 October 2018

A. Renaud  and
A. Venaille Open the ORCID record for A. Venaille [Opens in a new window]
A. Renaud*
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
A. Venaille
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
*
†Email address for correspondence: [email protected]
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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 been thoroughly 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 larger time. Using a Wentzel–Kramers–Brillouin 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.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 71 - 90
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Copyright
© 2018 Cambridge University Press 

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