Excitation of low frequency oscillations in a planetary magnetosheath by supersonic shear flow

We show that the slow magnetosonic (SM) perturbations generated in the vicinity of the magnetopause, due to the excitation of the Kelvin-Helmholtz (K.-H.) instability in the case of a supersonic flow velocity, are transformed into fast magnetosonic (FM) waves which can propagate into the magnetosheath. Under the conditions discussed in this paper, the FM wave has negative energy in the stationary (magnetospheric) coordinate frame. Due to this the outgoing FM wave increases the growth rate of the K.-H. instability excited at the magnetopause. Within the linear theory, we investigate the influence of the excited FM wave on the growth rate of the K.-H. instability. Simultaneously we predict the transformation of the SM mode into kinetic Alfvén (KA) mode. Thus, in general, two types of waves with different polarizations (the KA wave and the FM wave) should appear in the magnetosheath due to the excitation of the K.-H. instability. At the same time, the SM perturbations are only present in the localized region where the K.-H. instability is excited. To correctly describe the excitation of waves, we use two-fluid (for electrons and ions) magnetohydrodynamics. This approach is more general than the ideal magnetohydrodynamics and allows us to take into account the effects associated with the finite Larmor radius of ions. Also it can be used to investigate the K.-H. instability in a multi-component plasma, or in the case where the frequency of perturbations is of the order of the gyrofrequency of oxygen ions which may occur, for example, at the magnetosheath of Mars