Hamiltonian formalism and the Garrett-Munk spectrum of internal waves in the ocean - art. no. 168501

Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on a natural Hamiltonian description. A kinetic equation a ppropriate 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 c lose to the high wave-number limit of the Garrett-Munk spectrum of long int ernal waves in the ocean. In fact, a small modification of the Garrett-Munk formalism includes a spectrum consistent with the one predicted by wave tu rbulence.