On Kelvin–Helmholtz instability due to the solar wind interaction with unmagnetized planets

In this paper, the Kelvin–Helmholtz instability is studied by solving the ideal MHD equations for a compressible plasma. A transition layer of finite thickness between two plasmas, across which the magnitude of the velocity and the density change, is assumed. Growth rates are presented for the transverse case, i.e., the flow velocity is perpendicular to the magnetic field. If only the velocity changes across the boundary layer and the density is kept constant, an important quantity affecting the growth of the Kelvin–Helmholtz instability is the magnetosonic Mach number, which characterizes compressibility. The growth rates for the case when both, the velocity and the density, change are very sensitive to the ratio of the upper plasma density to the lower plasma density: a decrease of the density ratio yields a decrease of the growth rate. Including a density profile is very important for the application of the Kelvin–Helmholtz instability to the solar wind flow around unmagnetized planets, e.g., Venus, where the plasma density increases from the magnetosheath to the ionosphere.