The energy flux spectrum of internal waves generated by turbulent convection

TL;DR

This study uses 3D simulations to analyze how turbulent convection generates internal waves and their energy spectrum, confirming theoretical predictions about wave flux scaling and decay with distance.

Contribution

It provides the first direct numerical validation of the wave energy flux spectrum and decay laws in turbulent convection-driven internal waves.

Findings

Wave energy flux spectrum scales as $k_{ot}^4f^{-13/2}$ for weakly-damped waves.

Total wave energy flux decreases with distance as $z^{-13/8}$.

Simulations agree with existing theoretical models at high Rayleigh numbers and stratification.

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-V\"{a}is\"{a}l\"{a} 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 $k_{\perp}^4f^{-13/2}$ 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 $z^{-13/8}$.