Manifestations of Kelvin-Helmholtz instability in the solar atmosphere, solar wind and geomagnetosphere

We present the modern views on the nature of the Kelvin-Helmholtz (KH) instability and its manifestations in plasma of the solar corona, interplanetary medium and at the boundary of the geomagnetosphere. We briefly describe the main theoretical results of KH instability obtained in the linear approximation. When analyzing the observational data that confirm the occurrence of the KH instability in various magnetic formations of the solar coronal plasma, we use the classical results obtained in the incompressibility approximation. The same approach is used to describe the instability on the daytime magnetosphere boundary. Special attention is paid to the effect of compressibility when analyzing the instability of supersonic shear flows in the solar wind (SW) and on the geomagnetic tail boundary. At supersonic shear flows, disturbances with the wave vector parallel to flow velocity vector are known to be stable in the tangential discontinuity approximation [Landau, 1944]. Therefore, supersonic shear flows are considered to be stable in most studies that take only parallel disturbances into account. Our study takes into consideration the oblique disturbances inclined relative to the velocity vector and shows their crucial role in the instability of supersonic shear flows. The phase velocity of oblique disturbances is shown to be substantially less than the flow velocity, and values of the increment and frequency range are considerably greater than those of longitudinal disturbances. We emphasize that the magnetic field and plasma density inhomogeneity, which reduce the KH instability of subsonic shear flows, also reduce the stabilizing effect of compressibility of the medium and can significantly reduce the increment in the case of supersonic velocity difference. Effective excitation of oblique disturbances by the supersonic KH instability explains the existence of magnetosonic waves and the formation of diffuse shear flows in SW and on the boundary of the distant magnetotail, as well as the SW-magnetosphere energy and impulse transfer.