Journal of Fluid Mechanics
The energy flux spectrum of int...
10 November 2018 , R3
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)
1CNRS, Aix Marseille Univ, Centrale Marseille, IRPHE, Marseille, France
2Princeton Center for Theoretical Science, Princeton, NJ 08544, USA
DOI: https://doi.org/10.1017/jfm.2018.669
Published online by Cambridge University Press: 10 September 2018
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 $z^{-13/8}$ .
†Email address for correspondence: louisalexandre.couston@gmail.com
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JFM classification
Geophysical and Geological Flows: Geophysical and Geological Flows
Geophysical and Geological Flows: Internal waves
Turbulent Flows: Turbulent convection
Type Description Title
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.
Video (304.0 MB)