Thermal convection in a rotating layer of a magnetic fluid

Thermal convection in magnetic fluids can be driven by buoyancy or by magne tic forces (due to the thermomagnetic effect). Depending on the direction o f the applied temperature gradient, buoyancy effects: can be stabilizing (h eating from above) or destabilzing (heating from below), whereas the magnet ic forces always play a destabilizing role for magnetic fields perpendicula r to the interface. We investigate the influence of rotations using both li near and weakly non linear analyses of the governing hydrodynamic equations in the Boussinesq approximation. With a linear stability analysis we deter mine 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 dis cuss the validity of the assumptions entering the calculations for stress f ree boundaries. In the case of free boundary conditions, asymptotic express ions of the critical values for high rotation rates are derived. When the s ystem 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 describ ed by asymptotic expressions. We derive envelope equations for convection p atterns characterized by both: one wave vector and two competing wave vecto rs of equal length but different directions. These equations show that the system always exhibits a forward bifurcation. The well-known Kuppers-Lortz instability is also present in magnetic fluids. This instability sets in at critical values for a sufficiently high rotation rate. In simple fluids th e angle alpha 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 fiel d). There is also a weak dependence on the other magnetic parameters of the system. For a commercially available magnetic fluid this angle can be incr eased by approximately 10 degrees - 15 degrees compared to the simple fluid case.