Resonant instability of tangential discontinuity in a compressible fluid

The excitation and stability of surface waves on the interface of two compressible fluids moving with respect to each other in a two-dimensional channel is investigated. It is shown that in this case surface waves are always unstable. On the other hand, in this case the dispersion relation in the short and the long wavelength limits coincides with the dispersion relation in the compressible and the incompressible infinite fluid, respectively. Furthermore, surface wave excitation under resonant condition is investigated. It is concluded that due to the Cerenkov-like emission mechanism a sound wave propagates in the fluid at rest. In this case, the growth rate of the Cerenkov-like instability is compared with the growth rate of the instability for the excitation of the tangentially discontinuous surface wave. Likewise, using fluent software, surface wave excitation in two dimensions is simulated.