Kelvin‐Helmholtz instability of the magnetospheric boundary in a three‐dimensional global MHD simulation during northward IMF conditions

Abstract

We present results of a global, fully three‐dimensional, high‐resolution magnetohydrodynamic (MHD) simulation of the magnetosphere during steady northward interplanetary magnetic field (IMF) conditions. We investigate the stability of the magnetospheric boundary with respect to the growth of the Kelvin‐Helmholtz instability (KHI) driven by the velocity shear between the nearly stagnant magnetospheric plasma and the magnetosheath flow past it. We find the magnetospheric boundary to be globally unstable, including the high‐latitude boundary layer (meridional plane), where magnetic tension is not sufficient to stabilize the growth of oscillations. Roughly beyond the terminator, global modes coupled into the surface modes become most apparent, so that the entire body of the magnetosphere is engaged in an oscillatory motion. The wave vector of the surface oscillations has a component perpendicular to the background flow and tangential to the shear layer (in the equatorial plane, kz component of the wave vector), which is consistent with the generation of field‐aligned currents that flow on closed field lines between the inner portion of the boundary layer and the ionosphere. The distribution of wave power in the equatorial plane is consistent with the existence of a double‐vortex sheet, with vortex trains propagating along the inner and outer edges of the boundary layer. The double‐vortex sheet is most apparent in the simulation past the terminator plane but is transient and appears to be unstable and is most likely a consequence of nonlinear development of the velocity shear layer with a finite width. For the simulation with the solar wind velocity of 600 km/s, we find the width of the layer to be Δ≈1 RE at the terminator and the phase speed there to be similar to half of the total velocity drop across the layer (∼440 km/s), which is expected for a shear layer with uniform background density. We calculate the spatial growth rate for the dominant frequency mode in this region (∼4.4 mHz) to be ∼0.19RE−1, which is in excellent agreement with linear theory. For this mode, we find kΔ≈0.9, where k is the wave number, which corresponds to the fastest growing mode predicted by the linear theory. Finally, we find that the plasma compressibility is a key factor in controlling the growth rate of the KHI at the magnetosphere flanks in our simulation.