2D Internal Gravity Wave Turbulence

TL;DR

This paper classifies regimes of 2D stratified fluid turbulence using wave theory, confirms predictions with simulations, and explains layer formation through inverse energy cascades and wave interaction discreteness.

Contribution

It provides the first DNS confirmation of wave turbulence theory for internal gravity waves and characterizes different turbulence regimes in 2D stratified flows.

Findings

Weak wave turbulence spectrum matches kinetic theory predictions.

Layer formation occurs at strong stratification with spectral peaks at low frequencies.

Layer thickness and flow velocity are predicted from control parameters.

Abstract

Using weak wave turbulence theory analysis, we distinguish three main regimes for 2D stratified fluids in the dimensionless parameter space defined by the Froude number and the Reynolds number: discrete wave turbulence, weak wave turbulence, and strong nonlinear interaction. These regimes are investigated using direct numerical simulations (DNS) of the 2D Boussinesq equations with shear modes removed. In the weak wave turbulence regime, excluding slow frequencies, we observe a spectrum that aligns with recent predictions from kinetic theory. This finding represents the first DNS-based confirmation of wave turbulence theory for internal gravity waves. At strong stratification, in both the weak and strong interaction regimes, we observe the formation of layers accompanied by spectral peaks at low discrete frequencies. We explain this layering through an inverse kinetic energy cascade and the discreteness of wave-wave interactions at large scales. This analysis allows us to predict the layer thickness and typical flow velocity in terms of the control parameters.