A nonlinear stability analysis for rotating magnetized ferrofluid heated from below

A nonlinear (energy) stability analysis is performed for a rotating magnetized ferrofluid layer heated from below, in the stress-free boundary case. By introducing a generalized energy functional, a rigorous nonlinear stability result for a thermoconvective rotating magnetized ferrofluid is derived. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M3, and rotation parameter, TA1TA1, on subcritical instability region has also been analyzed. It is shown that with the increase of magnetic parameter, M3, the subcritical instability region between the two theories decreases quickly while with the increase of Taylor number, TA1TA1, the subcritical region expands a little for small values of TA1TA1 and expands significantly for large values of TA1TA1. We also demonstrate coupling between the buoyancy and magnetic forces in the presence of rotation in the nonlinear energy stability analysis as well as in linear instability analysis.