Anomalous transport by magnetohydrodynamic Kelvin‐Helmholtz instabilities in the solar wind‐magnetosphere interaction

Abstract

A magnetohydrodynamic simulation of Kelvin‐Helmholtz instabilities in a compressible plasma has been performed for parallel (v0∥B0) and transverse (v0⊥B0) configurations, modeling high‐latitude (or downstream flanks) and dayside low‐latitude magnetospheric boundaries. In the parallel configuration, a super‐Alfvénic and transsonic shear flow (with 2 < MA = V0/υA < 4 and Ms = V0/cs = 1, where V0 is the total jump of the velocity across the velocity shear layer) leads to an oscillation of the velocity shear layer, which bends the initial uniform magnetic field. With a hyper‐Alfvénic shear flow (MA > 4), the instability develops into a more turbulent state and the initial parallel shear flow develops into small eddies, which strongly twist, compress, and hence amplify the magnetic field by a dynamo action with an amplification factor MA/2. In the nonlinear stage, however large the initial Alfvén Mach number MA may be, the magnetic field, amplified and twisted by the hydromagnetic flow vortices, eventually reacts back upon the flow evolution, and the flow vortices cascade into smaller scale structures. In the transverse configuration, for a fast magnetosonic Mach number Mf (= V0/(cs² + υA²)1/2) greater than a critical Mach number, the instability leads to the formation of a fast shock discontinuity from an initially subfast shear flow. Anomalous tangential stress in the transverse configuration reaches 0.01ρ0V0², and the energy flux across the boundary in the magnetospheric inertial frame reaches as much as 2% of the magnetosheath flow kinetic energy flux, ½ρV0³; this viscous tangential stress could account for the convection potential drop over the polar cap of 10–30 kV. The anomalous (eddy) viscosity νano becomes >10−2 ΔV0, where Δ is the thickness of the initial velocity shear layer, and becomes as large as or even larger than the Bohm diffusion for conditions typical at the magnetospheric boundary, thereby satisfying the requirements of the “viscouslike” interaction hypothesis by Axford and Hines (1961). In the parallel configuration, the slow rarefactive wave (or Alfvén wave in the incompressible limit) is excited by the instability and contributes to a strong anomalous diffusion of momentum or a dissipation of vorticity by the magnetic viscosity (Maxwell stress); this in turn gives rise to momentum and energy fluxes and an anomalous viscosity 2–3 times larger than those brought about by the hydrodynamic Reynolds stress in the transverse configuration and hence provides a very efficient viscous interaction at the magnetospheric boundary.