Evaluations of wave-wave interactions for the oceanic internal gravity wave field at very high grid resolution

Internal gravity waves (IGWs) play a key role in ocean dynamics by interacting with mesoscale eddies, topography, and other waves, leading to wave breaking and mixing that influence small and large-scale circulations. Despite local variability, the IGW energy distribution exhibits a remarkably universal spectral shape, the Garrett-Munk (GM) spectrum, within which we study the scattering of IGWs via wave-wave interactions under the weak-interaction assumption.

We use the kinetic equation derived from a non-hydrostatic Boussinesq system with constant rotation and stratification. By developing Julia-native numerical codes, we evaluate the energy transfers for resonant and non-resonant interactions. Our results confirm that resonant triads dominate energy transfers, while non-resonant interactions are negligible in isotropic spectra but can contribute under anisotropic conditions. We show that the Boltzmann rates are small such that the weak-interaction assumption is satisfied. We find non-local interactions to be essential to understand the energy transfers within the IGW field, while local interactions are of minor importance. Parametric subharmonic instability drives a forward energy cascade in vertical wavenumber and an inverse cascade in frequency. Induced diffusion emerges as a primary energy transfer to small scales, and elastic scattering plays a similar but weaker role. We also find a new interaction mechanism, the third parametric generation, which provides a forward energy cascade in frequency and vertical wavenumber. We assess the convergence of the kinetic equation by introducing a cutoff in the IGW energy spectrum, or with a change in slope mimicking the transition to turbulence. Our findings provide convergent results at reduced computational costs, improving the efficiency and reliability of energy transfer evaluations in oceanic IGW spectra.