Resonant and non-resonant wave-wave interactions for internal gravity waves

An investigation has been conducted of the means by which energy is transferred among internal gravity waves. In weakly interacting flows, this is characterized by resonant interactions in which the interaction time scale is much greater than the component wave periods. The two-dimensional internal gravity wave equations of motion are given and solved by two different methods, the first of which involves a truncated Fourier series in which three or four resonantly interacting waves are treated, while in the second a finite difference integration of the equations of motion allows the resolution of many waves and a subgrid scale parameterization scheme is used for the modeling of dissipation due to wave overturning.