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Mean flows induced by inertia–gravity waves in a vertically confined domain

Published online by Cambridge University Press:  11 March 2020

Wenjing Dong Open the ORCID record for Wenjing Dong [Opens in a new window] ,
Oliver Bühler Open the ORCID record for Oliver Bühler [Opens in a new window]  and
K. Shafer Smith Open the ORCID record for K. Shafer Smith [Opens in a new window]
Wenjing Dong*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, NY 10012, USA
Oliver Bühler
Affiliation:
Courant Institute of Mathematical Sciences, New York University, NY 10012, USA
K. Shafer Smith
Affiliation:
Courant Institute of Mathematical Sciences, New York University, NY 10012, USA
*
†Email address for correspondence: wenjingdong11@hotmail.com
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Abstract

The Lagrangian-mean motion of fluid particles induced by horizontally localized small-amplitude wavepackets of vertically trapped inertia–gravity waves is computed analytically, at second order in wave amplitude, and the results are supported by direct nonlinear numerical simulations. The leading-order motion is assumed to be inertia–gravity waves, which is applicable to oceanic mesoscale flows in regions where wave activity is as strong as or stronger than the balanced flow. The analytical computation is based on time-dependent asymptotic wave–mean interaction theory, and the numerical simulation uses a Galerkin-truncated $f$-plane nonlinear hydrostatic Boussinesq model that retains the barotropic mode and two baroclinic modes (vertical wavenumbers 0, $m$ and $2m$), this being the minimal set on which consistent wave–mean interactions can take place. Two novel dynamical effects are revealed: First, we find that the barotropic component robustly dominates the Lagrangian-mean flow response, which is contrary to earlier findings for the same problem. Second, we discovered a new wavepacket regime in which the baroclinic mean-flow response consists of the persistent radiation of resonantly forced secondary internal waves. The latter effect occurs in an oceanically accessible parameter regime.

JFM classification

Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Dong et al. supplementary movie

The time evolution of Lagrangian baroclinic velocity v^L_2$.

Download Dong et al. supplementary movie(Video)
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