Thermal convection in a rotating layer of a magnetic fluid

Thermal convection in magnetic fluids can be driven by buoyancy or by magnetic forces (due to the thermomagnetic effect). Depending on the direction of the applied temperature gradient, buoyancy effects can be stabilizing (heating from above) or destabilizing (heating from below), whereas the magnetic forces always play a destabilizing role for magnetic fields perpendicular to the interface. We investigate the influence of rotations using both linear and weakly non-linear analyses of the governing hydrodynamic equations in the Boussinesq approximation. With a linear stability analysis we determine the values of the wavelength and the temperature gradient at the onset of convection (critical values). These are calculated analytically in the case of stress free boundaries and numerically for rigid boundaries. We discuss the validity of the assumptions entering the calculations for stress free boundaries. In the case of free boundary conditions, asymptotic expressions of the critical values for high rotation rates are derived. When the system is heated from above and the magnetic forces only slightly exceed the buoyancy forces, linear results show that both the critical wavelength and the critical temperature gradient diverge. Again, this behavior is described by asymptotic expressions. We derive envelope equations for convection patterns characterized by both: one wave vector and two competing wave vectors of equal length but different directions. These equations show that the system always exhibits a forward bifurcation. The well-known Küppers-Lortz instability is also present in magnetic fluids. This instability sets in at critical values for a sufficiently high rotation rate. In simple fluids the angle α depends only on the Prandtl number of the fluid. We show that for magnetic fluids this angle can be changed by changing the ratio of the buoyancy forces to the magnetic forces (i.e. by changing the magnetic field). There is also a weak dependence on the other magnetic parameters of the system. For a commercially available magnetic fluid this angle can be increased by approximately 10◦ – 15◦ compared to the simple fluid case. PACS. 75.50.Mm Magnetic liquids – 47.54.+r Pattern selection; pattern formation – 05.70.Ln Nonequilibrium and irreversible thermodynamics