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Nonlinear interaction and breaking of internal ocean waves are responsiblefor much of the interior ocean mixing, affecting ocean carbon storage and theglobal overturning circulation. These interactions are also believed to dictatethe observed Garrett-Munk wave energy spectrum, which is still unexplainedafter 50 years of studies. According to the resonant wave interactionapproximation, used to derive the kinetic equation for the energy spectrum, thedominant interactions are between wave triads whose wavevectors satisfy$\mathbf{k}=\mathbf{p}+\mathbf{q}$, and whose frequencies satisfy$\omega_{\mathbf{k}}=|\omega_{\mathbf{p}}\pm\omega_{\mathbf{q}}|$. In order totest the validity of the resonant wave interaction approximation, we examineseveral analytical derivations of the theory. The assumptions underlying eachderivation are tested using idealized direct 2d numerical simulations,representing near-observed energy levels of the oceanic internal wave field. Weshow that the assumptions underlying the derivations are not consistent withthe simulated dynamics. In addition, most of the triads satisfying the resonantconditions do not contribute significantly to nonlinear wave energy transfer inour simulations, while some interactions that are dominant in nonlinear energytransfers do not satisfy the resonance conditions. We also point to possibleself-consistency issues with some derivations found in the literature.

Is the resonant wave interaction approximation consistent with the dynamics of internal wave fields?