Distinguished regimes of 2-D internal gravity wave turbulence

Using weak wave turbulence theory analysis, we distinguish three main regimes for two-dimensional (2-D) 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 simulation (DNS) of the 2-D 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 attribute this layering to an inverse kinetic-energy transfer in combination with discrete 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.