Global stability results for temperature modulated convection in ferrofluids

The evolution of the energy functional in a dynamical system which arises from the stability of the time periodic temperature modulated state of the Rayleigh–Bénard convection in a horizontal thin fluid layer; results in a deviation of the critical nonlinear stability boundary from the linear instability boundary. If the fluid under consideration is magnetically polarizable, the deviation is further controlled by an interplay between the thermomagnetic effects and the modulation. A comprehensive study of this important stability problem is carried out theoretically and numerically using relative-stability theory. The critical Rayleigh number as predicted by the three theories: the relative stability, the conventional energy stability, and the linear instability theory; are shown to be different under the presence of modulation. A comparison of these theories on the basis of their predictions reveals that the global stability results correspond to the ‘relative stability boundary’ under modulation irrespective of whether the fluid under consideration is a ferrofluid or a non-magnetizable fluid. We also obtain the global stability results for the gravity free limit and the low and high frequency modulation.