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The energy flux spectrum of internal waves generated by turbulent convection

  • Louis-Alexandre Couston (a1), Daniel Lecoanet (a2), Benjamin Favier (a1) and Michael Le Bars (a1)
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 $z^{-13/8}$ .

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Corresponding author
Email address for correspondence: louisalexandre.couston@gmail.com
References
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Journal of Fluid Mechanics
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VIDEO
Supplementary materials

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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