Abstract
The stability under small disturbances is investigated of the two-dimensional laminar motion of an electrically conducting fluid under a transverse magnetic field. It is found that the dominating factor is the change in shape of the undisturbed velocity profile caused by the magnetic field, which depends only on the Hartmann number
M
. Curves of wave number against Reynolds number for neutral stability are calculated for a range of values of
M
; for large values of
M
the calculations are similar to those which determine the stability of ordinary boundary-layer flow. The critical Reynolds number is found to rise very rapidly with increasing
M
, so that a transverse magnetic field has a powerful stabilizing influence on this type of flow.
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