A New Analysis of the Vortex-Size-Dependent Growth Rate of Kelvin-Helmholtz Instability

Abstract:

Kelvin-Helmholtz (K-H) instability is an important process for mass transport at the flank magnetopause during northward interplanetary magnetic field. Previous theoretical studies conclude that the development of the K-H instability should base on the most unstable mode, which is a function of the shear-flow Mach number, but is independent of the location of the unperturbed boundary. However, simulations of subsonic velocity shear indicate that the amplitude and wavelength of the vortices expand with time, but the growth rate of the K-H instability is relatively unchanged. We suspect that the growth rate of different wavelength should depend on the location of the unperturbed boundary. In this study, we examine the growth rate of the K-H instability with subsonic velocity shear as a function of Mach number, wavelength, and the location of the unperturbed boundary. Our results indicate that for a given Mach number, the growth rate increases but the wavelength of the most unstable wave mode decreases with increasing distance from the unperturbed boundary from the center of the surface wave. Namely, if the wavelength of the surface wave increases with increasing amplitude of the surface wave, the growth rate could remain unchanged for a period. As a result, the most unstable mode could be irrelevant to the observed wavelength of the surface wave. Our results provide a good theoretical explanation of the evolution of K-H instability found in simulations and observations.