Linear theory of the Kelvin‐Helmholtz instability in the low‐latitude boundary layer

Abstract

We examine the stability of the magnetospheric low‐latitude boundary layer to the Kelvin‐Helmholtz instability taking into account the finite thickness of the velocity shear layer, the relative thickness and position of the “current” layer in which the magnetic field rotates from magnetosheath to magnetospheric configurations, and the collisionless and anisotropic nature of the plasmas therein. We show that three factors enhance the instability: (1) a decrease in the thickness of the shear layer, (2) a decrease in the thickness of the current layer (relative to the shear layer), and (3) the proximity of the “current layer” to the outer edge of the shear layer. Although the maximum growth rate occurs for wave numbers roughly equal to the inverse of the semithickness of the shear layer, the velocity threshold for the onset of the instability is insensitive to the thickness. However, when the current layer is displaced from the center toward the outer edge of the shear layer, the threshold is dramatically reduced and the boundary layer can be rendered unstable by relatively small shear flows, suggesting that even the region close to the subsolar point could become unstable when the sheath flow is perpendicular to the magnetospheric magnetic field. This mode can be identified by characteristic profiles across the boundary layer: the plasma density, pressure, and magnetic field strength perturbations all peak near the center of the boundary layer. The transverse magnetic field fluctuations are largest around the current layer, while the radial motions dominate near the inner edge of the boundary layer.