Nonlinear Interaction of Gravity and Acoustic Waves - Teruya, André Seiji Wakate (2019)
Here we have investigated the possibility of an inertio-acoustic wave-mode to be unstable with regard to gravity mode perturbations through nonlinear triad interactions in the context of a shallow nonhydrostatic model. We have considered highly truncated Galerkin expansions of the perturbations around a resting, hydrostatic and isothermal background state in terms of the eigensolutions of the linear problem. For a single interacting wave triplet, we have shown that an acoustic mode cannot amplify a pair of inertio-gravity perturbations due to the high mismatch among the eigenfrequencies of the three interacting wave-modes, which resquires an unrealistically high amplitude of the acoustic mode in order for pump wave instability to occur. In contrast, it has been demonstrated by analyzing the dynamics of two triads coupled by a single mode that a non-hydrostatic gravity wave-mode participating of a nearly resonant interaction with two acoustic modes can be unstable to small amplitude perturbations associated with a pair of two hydrostatically balanced inertio-gravity wave-modes. This linear instability yields significant inter-triad energy exchanges if the nonlinearity associated with the second triplet containing the two hydrostatically balanced inertio-gravity modes is restored. Therefore, this inter-triad energy exchanges lead the acoustic modes to yield significant energy modulations in hydrostatic inertio-gravity wave modes. The implications of the results for the nonlinear hydrostatic adjustment problem are discussed.