Stability of an external gravity wave in a stratified basic flow with lateral shear

The author investigates the stability of an external gravity wave progressing horizontally in an inviscid and incompressible stratified basic flow with lateral shear. (1) In the model which basic flow has a Helmholtz velocity profile, there exist no neutral solutions contrary to internal gravity waves. Perturbations are always unstable independent of the coefficient of vertical wave mode m or the wave number k_y. (2) In the model which basic flow is composed of unbounded layers with the central shear zone, the stability is subject to the relation of m, k_y and width of shearing layer 2h. The linear shear α affects only a damping or a growing factor. (a) In the case of k_y ≧ m, there exist a neutrally stable solution k_y = √. The region k_y > √ is stable, and the region m ≦ k_y is unstable. (b) In the case of m > k_y, there exist two traveling modes, a damping mode and a growing mode. So perturbations are unstable. And if m >> k_y they can be stable