Nonlinear interaction of internal gravity waves

This investigation concerns the weak transfer of energy in various models of the internal wave spectrum by nonlinear resonant interaction of triads of waves whose wavenumbers and frequencies satisfy K1 plus or minus K2 = K and (omega 1) plus or minus (omega 2) = omega. Three limiting cases of triads with widely disparate wavenumber, frequencies, or both, which we designate induced diffusion, elastic scattering, and subharmonic instability, dominate the numerically computed transfers of a contrived spectrum of possible relevance to the atmosphere and three models of the oceanic internal wave spectrum by Garrett and Munk. The diffusive mechanism predicts equilibrium spectra which are in general agreement with the two latest GM models of oceanic observations at high wavenumber. This diffusion mechanism is applicable to interaction of internal waves with the background flow as well. The basic result is that special, simplified cases of resonant interactions are important in determining some of the gross features of the internal wave spectrum.