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Long-time dynamics of internal wave streaming

Published online by Cambridge University Press:  17 November 2020

Timothée Jamin Open the ORCID record for Timothée Jamin [Opens in a new window] ,
Takeshi Kataoka Open the ORCID record for Takeshi Kataoka [Opens in a new window] ,
Thierry Dauxois Open the ORCID record for Thierry Dauxois [Opens in a new window]  and
T. R. Akylas Open the ORCID record for T. R. Akylas [Opens in a new window]
Timothée Jamin
Affiliation:
Laboratoire de Physique, Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Lyon, France
Takeshi Kataoka
Affiliation:
Department of Mechanical Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe657-8501, Japan
Thierry Dauxois
Affiliation:
Laboratoire de Physique, Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Lyon, France
T. R. Akylas*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

The mean flow induced by a three-dimensional propagating internal gravity wave beam in a uniformly stratified fluid is studied experimentally and theoretically. Previous related work concentrated on the early stage of mean-flow generation, dominated by the phenomenon of streaming – a horizontal mean flow that grows linearly in time – due to resonant production of mean potential vorticity in the vicinity of the beam. The focus here, by contrast, is on the long-time mean-flow evolution. Experimental observations in a stratified fluid tank for times up to $t=120T_0$, where $T_0$ is the beam period, reveal that the induced mean flow undergoes three distinct stages: (i) resonant growth of streaming in the beam vicinity; (ii) saturation of streaming and onset of horizontal advection; and (iii) establishment of a quasi-steady state where the mean flow is highly elongated and stretches in the along-tank horizontal direction. To capture (i)–(iii), the theoretical model of Fan et al. (J. Fluid Mech., vol. 838, 2018, R1) is extended by accounting for the effects of horizontal advection and viscous diffusion of mean potential vorticity. The predictions of the proposed model, over the entire mean-flow evolution, are in excellent agreement with the experimental observations as well as numerical simulations based on the full Navier–Stokes equations.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A2
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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