On the kinetics of internal gravity waves beyond the hydrostatic regime

We present a new derivation of the kinetic equation for weak, non-hydrostatic internal gravity wave turbulence. The equation is equivalent to the one obtained by Caillol & Zeitlin ( Dyn. Atmos. Oceans , vol. 32, issue 2, 2000, pp. 81–112), but it takes a canonical form. We show that it conserves the energy without involving the resonance condition in frequency, and look for the isotropic part of the steady, scale-invariant solutions. We provide a parametrization of the resonant manifold of non-hydrostatic internal gravity wave triadic interactions. This allows us to simplify the collision integral, and to evaluate the transfer coefficients of all triadic interactions. In the hydrostatic limit, our equation is equivalent to the Hamiltonian description of Lvov & Tabak ( Phys. Rev. Lett. , vol. 87, issue 16, 2001, 168501).