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The wave-induced flow of internal gravity wavepackets with arbitrary aspect ratio

Published online by Cambridge University Press:  17 November 2017

T. S. van den Bremer Open the ORCID record for T. S. van den Bremer [Opens in a new window]  and
B. R. Sutherland Open the ORCID record for B. R. Sutherland [Opens in a new window]
T. S. van den Bremer*
Affiliation:
School of Engineering, University of Edinburgh, The King’s Buildings, Robert Stevenson Road, Edinburgh EH9 3FB, UK
B. R. Sutherland
Affiliation:
Departments of Physics, and Earth and Atmospheric Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2E3
*
†Email address for correspondence: [email protected]
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Abstract

We examine the wave-induced flow of small-amplitude, quasi-monochromatic, three-dimensional, Boussinesq internal gravity wavepackets in a uniformly stratified ambient. It has been known since Bretherton (J. Fluid Mech., vol. 36 (4), 1969, pp. 785–803) that one-, two- and three-dimensional wavepackets induce qualitatively different flows. Whereas the wave-induced mean flow for compact three-dimensional wavepackets consists of a purely horizontal localized circulation that translates with and around the wavepacket, known as the Bretherton flow, such a flow is prohibited for a two-dimensional wavepacket of infinite spanwise extent, which instead induces a non-local internal wave response that is long compared with the streamwise extent of the wavepacket. One-dimensional (horizontally periodic) wavepackets induce a horizontal, non-divergent unidirectional flow. Through perturbation theory for quasi-monochromatic wavepackets of arbitrary aspect ratio, we predict for which aspect ratios which type of induced mean flow dominates. We compose a regime diagram that delineates whether the induced flow is comparable to that of one-, two- or compact three-dimensional wavepackets. The predictions agree well with the results of fully nonlinear three-dimensional numerical simulations.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 834 , 10 January 2018 , pp. 385 - 408
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Copyright
© 2017 Cambridge University Press 

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