Wave-wave interactions in stratified fluids: A comparison between different approaches

Various approaches have been developed over the last four decades to characterize the magnitude of nonlinear interaction between triads of internal waves in stratified oceanographic flows. The present manuscript compares some of these approaches and demonstrates that, in the limit of long internal waves in hydrostatic balance and in the absence of rotation, these various approaches predict different rates of energy transfer between waves. Nevertheless, and somewhat surprisingly, under assumption of resonant wave-wave interactions, these approaches give equivalent results.