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The energy flux spectrum of internal waves generated by turbulent convection

Published online by Cambridge University Press:  10 September 2018

Louis-Alexandre Couston Open the ORCID record for Louis-Alexandre Couston [Opens in a new window] ,
Daniel Lecoanet ,
Benjamin Favier Open the ORCID record for Benjamin Favier [Opens in a new window]  and
Michael Le Bars
Louis-Alexandre Couston*
Affiliation:
CNRS, Aix Marseille Univ, Centrale Marseille, IRPHE, Marseille, France
Daniel Lecoanet
Affiliation:
Princeton Center for Theoretical Science, Princeton, NJ 08544, USA
Benjamin Favier
Affiliation:
CNRS, Aix Marseille Univ, Centrale Marseille, IRPHE, Marseille, France
Michael Le Bars
Affiliation:
CNRS, Aix Marseille Univ, Centrale Marseille, IRPHE, Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

We present three-dimensional direct numerical simulations of internal waves excited by turbulent convection in a self-consistent, Boussinesq and Cartesian model of mixed convective and stably stratified fluids. We demonstrate that in the limit of large Rayleigh number ($Ra\in [4\times 10^{7},10^{9}]$) and large stratification (Brunt–Väisälä frequencies $f_{N}\gg f_{c}$, where $f_{c}$ is the convective frequency), simulations are in good agreement with a theory that assumes waves are generated by Reynolds stresses due to eddies in the turbulent region as described in Lecoanet & Quataert (Mon. Not. R. Astron. Soc., vol. 430 (3), 2013, pp. 2363–2376). Specifically, we demonstrate that the wave energy flux spectrum scales like $k_{\bot }^{4}\,f^{-13/2}$ for weakly damped waves (with $k_{\bot }$ and $f$ the waves’ horizontal wavenumbers and frequencies, respectively), and that the total wave energy flux decays with $z$, the distance from the convective region, like $z^{-13/8}$.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Turbulent Flows: Turbulent convection
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 854 , 10 November 2018 , R3
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Copyright
© 2018 Cambridge University Press 

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References

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Couston et al supplementary material

Movie of (a) $w(y = 0)$, (b) $T_z-\bar{T}_z$ at $y = 0$ (overbar denotes x average), (c) $w(z = 0.7)$, (d) $w(z = 1:3)$ for simulation case $C_8^{400}$. Variables in the wave region $(z > 1)$ in (a), (b) have been multiplied by $10^4$, $10^3$, respectively.

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