Hamiltonian formalism and the Garrett-Munk spectrum of internal waves in the ocean

Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on a natural Hamiltonian description. A kinetic equation appropriate for the description of spectral energy transfer is derived, and its anisotropic self-similar stationary solution corresponding to a direct cascade of energy toward the short scales is found. This solution is very close to the high wave-number limit of the Garrett-Munk spectrum of long internal waves in the ocean. In fact, a small modification of the Garrett-Munk formalism includes a spectrum consistent with the one predicted by wave turbulence.