Experimental observations of internal wave turbulence transition in a stratified fluid

TL;DR

This study experimentally investigates how internal wave turbulence transitions in a stratified fluid are influenced by domain size and forcing, revealing different turbulence regimes and their relation to the buoyancy Reynolds number.

Contribution

It demonstrates how finite-size effects impact internal wave turbulence and identifies the regimes and transition criteria based on the buoyancy Reynolds number.

Findings

Wave turbulence observed when finite-size effects are minimized.

Spectral slopes align with Garrett-Munk spectra in turbulence regime.

Transitions between regimes are governed by the buoyancy Reynolds number.

Abstract

Recent developments of the weak turbulence theory applied to internal waves exhibit a power-law solution of the kinetic energy equation close to the oceanic Garrett \& Munk spectrum, confirming weakly nonlinear wave interactions as a likely explanation of the observed oceanic spectra. However, finite-size effects can hinder wave interactions in bounded domains, and observations often differ from theoretical predictions. This article studies the dynamical regimes experimentally developing in a stratified fluid forced by internal gravity waves in a pentagonal domain. We find that by changing the shape and increasing the dimensions of the domain, finite-size effects diminish and wave turbulence is observed. In this regime, the temporal spectra decay with a slope compatible with the Garrett-Munk spectra. Different regimes appear by changing the forcing conditions, namely discrete wave turbulence, weak wave turbulence, and strongly stratified turbulence. The buoyancy Reynolds number $Re_b$ marks well the transitions between the regimes, with weak wave turbulence occurring for $1\lesssim Re_b\lesssim 3.5$ and strongly non-linear stratified turbulence for higher $Re_b$.