Abstract
A study is made of the stability of a stratified shear flow in a perfectly conducting fluid in the presence of an external magnetic field aligned with the flow. A semi-circle theorem for the present hydromagnetic case is proved. The magnetic field is found to have a stabilizing effect on the flow. The Rayleigh-Taylor instability problem in a stratified conducting fluid is discussed. Finally, a study is made of the absorption of wave energy by the mean flow in the hydromagnetic case by considering a shear flow with an anti-symmetric velocity profile given byU=tanhz. Unlike the hydrodynamic case, it is found that, in the critical layer atU=0, the transfer of the wave energy to the mean flow occurs for any value of the Richardson number. This result implies again the stabilizing effect of the magnetic field on the shear flow.
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