A sufficient condition for instability in a sheared incompressible magnetofluid

It is shown that a sufficient condition for the stability of an incompressi ble sheared gravitationally stratified ideal magnetofluid with flow-aligned horizontal magnetic field is that there exists a Galilean frame in which t he Row is nowhere super-Alfvenic (similarly, stability is assured in a comp ressible sheer flow without gravity if there exists a frame in which the fl ow nowhere exceeds the cusp speed). Complex eigenvalue bounds are presented for unstable Rows. The stability condition is applied to the solar tachocl ine; it suggests that any shear instabilities associated with radial gradie nts in flow speed should be stabilized by fields of above about 7 kG.