Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. To investigate their dynamics, we perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy spectrum of weakly nonlinear internal gravity waves. During the early evolution, three well-known nonlocal interactions, the Elastic Scattering, the Induced-Diffusion, and the Parametric Subharmonic Instability, together with a Superharmonic Resonance play a prominent role. In contrast, local interactions are responsible for anisotropic energy cascade on longer time scales. We reveal emergence of a condensate at small horizontal wavevectors that can be interpreted as a pure wave-wave interaction-mediated layering process.

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