Patterns of thermomagnetic convection in magnetic fluids subjected to spatially modulated magnetic fields.

An analysis of thermomagnetic convection in a thin horizontal layer of magnetic fluid constrained horizontally by impermeable layers and subjected to a spatially and symmetrically modulated magnetic field is presented. The magnetic field as well as the temperature gradient are oriented vertically. For any nonzero magnetic field the base state is a convective one formed by a double vortex which reflects the symmetrical modulation. For long wave modulations the linear stability analysis reveals that the critical Rayleigh number Ra(c) for the stability of the base state against small disturbances increases with increasing magnetic driving force. An analytical expression for Ra(c) is derived which shows the characteristic feature of sudden jumps of Ra(c) at particular values of the magnetic driving force.