Wave-wave interactions within a typical internal gravity wave spectrum in the ocean

Internal gravity waves (IGWs) shape the ocean through their interactions with e.g. eddies and other waves. These interactions can lead to wave breaking and density mixing, which influence large-scale mean flows. The resulting energy transfers shape the spectral shape of IGWs, which is surprisingly similar throughout the oceans - the universal Garrett-Munk (GM) spectrum. A key mechanism shaping this continuous energy spectrum is nonlinear wave-wave interaction. We study the scattering of IGWs via wave-wave interactions under the weak-interaction assumption, using the kinetic equation derived from a non-hydrostatic Boussinesq system with constant rotation and stratification. The kinetic equation and coupling coefficients derived from Eulerian and Lagrangian equations are identical under the resonance condition. By developing Julia-native numerical codes, we evaluate the energy transfers for resonant and non-resonant interactions, including inertial and buoyancy oscillations. Our findings confirm that resonant triads dominate the energy transfers, while non-resonant interactions are negligible in isotropic spectra but may become relevant in anisotropic conditions. These findings provide convergent results at reduced computational costs, improving the efficiency and reliability of energy transfer evaluations in oceanic IGW spectra.