Resonant interaction of internal waves in a stratified shear flow

The resonant interactions among internal wave trains in a flow consisting of a middle layer of homogeneous fluid in linear shear flow and continguous upper and lower stratified layers of constant velocities are investigated. Three wave trains satisfying the dispersion relations and the so‐called resonant conditions, k1=k2+k3 and σ1=σ2+σ3, are considered graphically, and the resonant triads of the same mode are found to exist. Some multiple resonances, i.e., the resonant interactions among waves which are the members of different triads, are also found to happen. The explosive and decay instabilities of multiple resonances are considered qualitatively, and energy exchange is expected to occur among the resonant triads.