A magnetohydrodynamic simulation of Kelvin-Helmholtz instabilities in a compressible plasma has been performed for parallel (v0∥B0) and (v0⊥B0) configurations, modeling high-latitude (or downstream flanks) and dayside low-latitude magnetospheric boundaries. In the parallel configuration, a super-Alfv¿nic and transsonic shear flow (with 24), 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 Alfv¿n 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 into smaller scale structures. In the transverse configuraion, for a fast magnetosonic Mach number Mf(=V0/(cs2+vA2)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 reaches 0.01&rgr;0V22, and the energy flux across the boundary in the magnetospheric inertial frame reaches as much as 2% of the magnetoshearth flow kinetic energy, 1/2&rgr;V03; this vicsous tangential stress could account for the convection potential drop over the polar cap of 10--30 kV. The anomalous (eddy) viscosity vano becomes >10-2 ΔV0, where Δ is the thickness of the initial 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 Alfv¿n 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 as an anomalous viscosity 2--3 times larger than those brought by the hydrodynamic Reynolds stress in the transverse configuration and hence provides a very efficient viscous interaction at the magnetospheric boundary.