Experimental observations of internal wave turbulence transition in a stratified fluid

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 Re b 3.5 and strongly non-linear stratified turbulence for higher Re b .

Numerical study of experimentally inspired stratified turbulence forced by waves

“…We observe less marked peaks in this range, and a logarithmic scale representation (left panel of figure 23) shows that the spectral behaviour at those frequencies is compatible with a ω −2 Garrett and Munk spectrum [2]. A qualitatively similar spectrum could be described in experiments [15].…”

“…Frequency spectra qualitatively consistent with GM spectra were observed at frequencies greater than the forcing and extending at frequencies greater than N . This observation suggests the occurence of strongly non linear wave turbulence [15].…”

“…We performed numerical simulations of a stratified turbulent flow, using a forcing mechanism inspired by experiments done in the Coriolis facility [1,15]. The generated flows exhibited turbulent Froude numbers around 10 −3 and buoyancy Reynolds numbers ranging from 0.22 to 6.3.…”

“…The equations ( 14) and ( 15) are called the spectral energy budget equations. In stationary state, the time derivatives of both energy types are zero in average, and the statistics of the spectral quantities in the left hand side of equations ( 14) and (15) do not depend on time. We therefore compute the transfer and dissipation terms of the spectral energy budget and average them over the length of the time window for the run at resolution 1152 × 1152 × 192.…”

“…Recent experiments [1,15] have managed to generate strongly stratified turbulent flows by forcing large scale internal waves into a large scale tank (the Coriolis platform in Grenoble) filled with stratified salty water. A continuum of waves was observed, and key elements of WWT phenomenology were identified.…”