The energy flux spectrum of internal waves generated by turbulent convection

Abstract

We present three-dimensional direct numerical simulations of internal waves excited by turbulent convection in a self-consistent, Boussinesq and Cartesian model of convective--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 (Lecoanet \& Quataert 2013 MNRAS 430 (3) 2363-2376). Specifically, we demonstrate that the wave energy flux spectrum scales like $k_{\perp }^4{f}^{-13/2}$ for weakly-damped waves (with $k_{\perp }$ and $f$ the waves' horizontal wavenumbers and frequencies), and that the total wave energy flux decays with $z$, the distance from the convective region, like $z^{-13/8}$.

arXiv comment13 pages, 6 figures

References in corpus (9)

• Internal Gravity Waves in Massive Stars: Angular Momentum Transport
• Internal Gravity Waves Modulate the Apparent Misalignment of Exoplanets around Hot Stars
• Internal Gravity Wave Excitation by Turbulent Convection
• Generation of internal gravity waves by penetrative convection
• Intermittency of velocity time increments in turbulence
• Experimental observation of a strong mean flow induced by internal gravity waves
• Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves
• Dynamics of Mixed Convective--Stably-Stratified Fluids
• Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection

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