Resonant interactions of internal waves in atmospheric shear flows with the participation of marginally unstable modes

Three-wave resonant interactions of gravity-shear waves are analyzed in a t hree-layer model of an atmospheric stratified shear flow. A specific case w hen one of the waves is marginally unstable is discussed. It is shown that such wave interactions are responsible for an "explosive" instability of th e main flow, and its growth rate can be greater than that of an "explosive" instability arising from interactions of stable waves alone. Equations tha t describe the time dependence of the complex amplitudes of interacting wav es are derived for a certain general class of Hamiltonian dynamic systems. In particular, the system of equations describing wave dynamics in the thre e-layer model of shear flow under consideration belongs to this class.