Numerical study of experimentally inspired stratified turbulence forced by waves

TL;DR

This study uses numerical simulations to analyze stratified turbulence driven by internal waves, revealing flow regimes, energy transfer mechanisms, and the potential for experimental realization in large-scale setups like the Coriolis platform.

Contribution

It demonstrates the feasibility of producing stratified turbulence driven by waves in large experimental apparatus and characterizes the flow regimes and energy transfer processes.

Findings

Flow consists of large vortices, internal waves, and weaker waves outside modes.

Flow is in an intermediate regime with small horizontal Froude number and buoyancy Reynolds number near unity.

Upscale energy flux occurs when forcing frequency is just below the Brunt-V"ais"al"a frequency.

Abstract

Stratified flows forced by internal waves similar to those obtained in the Coriolis platform (LEGI, Grenoble, France) \cite{Savaro2020} are studied by pseudospectral triply-periodic simulations. The experimental forcing mechanism consisting in large oscillating vertical panels is mimicked by a penalization method. The analysis of temporal and spatiotemporal spectra reveals that the flow for the strongest forcing in the experiments is composed of two superposed large and quasi-steady horizontal vortices, of internal waves in box modes and of much weaker waves outside the modes. Spatial spectra and spectral energy budget confirm that the flow is in an intermediate regime for very small horizontal Froude number $F_h$ and buoyancy Reynolds number $R$ close to unity. Since the forcing frequency $\omega_f$ is just slightly smaller than the Brunt-V\"ais\"al\"a frequency $N$, there are energy transfers towards slower waves and large vortices, which correspond to an upscale energy flux over the horizontal. Two other experimentally feasible sets of parameters are investigated. A larger amplitude forcing shows that it would indeed be possible to produce in huge apparatus like the Coriolis platform stratified turbulence forced by waves for small $F_h$ and buoyancy Reynolds number $R$ of order 10. Forcing slower waves for $\omega_f = 0.40 N$ leaves space between $\omega_f$ and $N$ for "down-time-scale" transfers through weakly nonlinear interactions with temporal spectra consistent with $\omega^{-2}$ slope. However, for this set of parameters, the large scales of the flow are strongly dissipative and there is no downscale energy cascade.