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Simulating turbulent mixing caused by local instability of internal gravity waves

Published online by Cambridge University Press:  19 March 2021

Yohei Onuki Open the ORCID record for Yohei Onuki [Opens in a new window] ,
Sylvain Joubaud Open the ORCID record for Sylvain Joubaud [Opens in a new window]  and
Thierry Dauxois Open the ORCID record for Thierry Dauxois [Opens in a new window]
Yohei Onuki*
Affiliation:
Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
Sylvain Joubaud
Affiliation:
Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique, F-69342Lyon, France Institut Universitaire de France (IUF), France
Thierry Dauxois
Affiliation:
Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique, F-69342Lyon, France
*
†Email address for correspondence: onuki@riam.kyushu-u.ac.jp
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Abstract

With the aim of assessing internal wave-driven mixing in the ocean, we develop a new technique for direct numerical simulations of stratified turbulence. Since the spatial scale of oceanic internal gravity waves is typically much larger than that of turbulence, fully incorporating both in a model would require a high computational cost, and is therefore out of our scope. Alternatively, we cut out a small domain periodically distorted by an unresolved large-scale internal wave and locally simulate the energy cascade to the smallest scales. In this model, even though the Froude number of the outer wave, $Fr$, is small such that density overturn or shear instability does not occur, a striped pattern of disturbance is exponentially amplified through a parametric subharmonic instability. When the disturbance amplitude grows sufficiently large, secondary instabilities arise and produce much smaller-scale fluctuations. Passing through these two stages, wave energy is transferred into turbulence energy and will be eventually dissipated. Different from the conventional scenarios of vertical shear-induced instabilities, a large part of turbulent potential energy is supplied from the outer wave and directly used for mixing. The mixing coefficient $\varGamma =\epsilon _P/\epsilon$, where $\epsilon$ is the dissipation rate of kinetic energy and $\epsilon _P$ is that of available potential energy, is always greater than 0.5 and tends to increase with $Fr$. Although our results are mostly consistent with the recently proposed scaling relationship between $\varGamma$ and the turbulent Froude number, $Fr_t$, the values of $\varGamma$ obtained here are larger by a factor of about two than previously reported.

JFM classification

Turbulent Flows: Stratified turbulence Geophysical and Geological Flows: Internal waves Instability: Parametric instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A77
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Buoyancy perturbation on the model domain surface.

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