Kelvin‐Helmholtz instability at the magnetospheric boundary: Dependence on the magnetosheath sonic Mach number

It has recently been demonstrated, by means of a two-dimensional MHD simulation, that a finite thick velocity shear layer with super-Alfvrnic velocity jump at the magnetospheric boundary is unstable to the Kelvin-Helmholtz (K-H) instability no matter how large the magnetosheath sonic Mach number (Ms)' a result suggesting that the tail flank boundary of the magnetosphere is unstable to the K-H instability. In order to investigate this consequence further, the dependence of the development of the K-H instability on Ms is studied in detail. For all magnetosheath sonic Mach numbers a velocity boundary layer is formed by the instability inside of the magnetopause, and it becomes wider for a smaller magnetosheath sonic Mach number. A flow vortex is excited at the inner edge of the velocity boundary layer for all sonic Mach numbers, and the magnetopause boundary is more highly nonlinearly corrugated by the instability for a smaller sonic Mach number. The net energy and momentum flux densities into the magnetosphere are calculated just prior to the saturation stage' for 1.0 < M s < 3.0 the energy flux density into the magnetosphere is approximated by O.054MsPoCs3/2 = O.045VoPo (where P0 is the unperturbed magnetosheath plasma density, P0 is the unperturbed magnetosheath pressure, V0 is the unperturbed magnetosheath flow velocity, and Cs is the magnetosheath sound speed), and the momentum flux density into the magnetosphere or the tangential (shearing) stress at the boundary is approximated by 0.083p0. The anomalous viscosity by the instability decreases in the absolute magnitude with increasing Ms' this result suggests that the dayside (except the subsolar region) and the dawn-dusk magnetopauses, where the magnetosheath flow remains subsonic, are the most viscous parts of the boundary, although the tail flanks are also found to be viscous enough for the viscous interaction. The structure of the weak shock in the magnetosheath developed from the K-H instability and the asymptotic eigenmode structure of the instability are elucidated. The relevance of the simulation results to the viscous interaction and a ULF wave generation is finally discussed.