CRITERIA FOR SHEAR-FLOW INSTABILITY IN THE MAGNETOPAUSE BOUNDARY-LAYER REGION

Shear flow instability is studied in the planar magnetopause boundary layer region by treating the plasma as compressible. A necessary crite rion for instability near the Alfven resonance is obtained. Sufficient criterion for instability is derived from the solution of a six degre e polynomial for the cases of constant and antisymmetric velocity prof iles when there is no Alfven resonance. Both the criteria are obtained analytically for the first time. The necessary criterion generalises the well-known inflexion point theorem and Rayleigh's criterion in the hydrodynamic case to magnetohydrodynamic case for incompressible plas ma provided both the Alfven surfaces lie in the boundary layer. The Al fven resonant surfaces are similar to the boundary walls in hydrodynam ics. A semi-hyperbola theorem for the unstable situation is derived wh ich represents the domain of Doppler shifted real frequency and imagin ary frequency. From the sufficient criterion for instability it is obs erved that plasma shear should be more for a compressible plasma in or der to make the plasma unstable. The growth rate for instability is ob tained. A thin layer around Alfven resonance effectively determines ho w fast the flow could attain instability.