Rotating magnetic field effect on an onset of convection in a horizontal layer of conducting fluid

The onset of convection in a horizontal layer of an electrically conducting fluid heated from below is studied in the presence of a horizontal magnetic field rotating about a vertical axis. Two different ranges of the rotation frequency are considered: (1) the case of high frequencies of rotation for which the averaging approach is used and (2) the case of finite frequencies for which the averaging approach might be implemented. It is shown that in general the magnetic field stabilizes the static state of pure thermal conduction. However, there exists a parameter range where the inhomogeneity of the magnetic field is strong enough to provide energy for the growth of disturbances even if the fluid layer is stably stratified.