ON THE STATIONARY ENERGY-SPECTRA FOR UNIDIRECTIONALLY PROPAGATING INTERNAL GRAVITY-WAVES

Starting from the Euler equations in the Boussinesq approximation for a stratified fluid in two dimensions we establish a kinetic equation f or a statistical ensemble of weakly non-linear internal gravity waves propagating in the same horizontal direction. We find a transformation of this equation to a standard form adopted in the weak turbulence th eory and then, limiting ourselves to high vertical-low horizontal wave number waves, get equilibrium (Rayleigh-Jeans) and non-equilibrium (Ko lmogorov) stationary energy spectra, among them a k(-3) vertical waven umber spectrum.