Influence of magnetic field modulation on thermomagnetic convection in a layer of ferrofluid bounded by rigid–free boundaries

With a focus on rigid–free boundaries, the impact of magnetic field modulation on thermomagnetic convection in ferrofluids is studied. The effects of large and small-scale modulations are examined using linear theory. Utilizing the superposition principle and several perturbation modes, small-scale modulation is investigated. The case of large-scale modulation is dealt with the aid of Mathieu equation to shed light on the prevalence of subharmonic motions. Utility of Floquet theory resulted in an infinite linear system from which the critical magnetic Rayleigh number was evaluated in the case of large-scale modulations. Weak non-linear theory is used in arriving at the non-autonomous tri-modal Lorenz system, from which bifurcation and post-convective analyses are done. It was found that magnetic field-modulation has significant, yet varying stabilizing effects on the convection process, and is uniquely determined by the conditions of the medium and magnitude of the modulation. Another important outcome of the study is that magnetic field modulation induces hyperchaos within the tri-modal autonomous system, and occurs for random combinations of modulation parameters. The emergence of chaos for rigid–free boundaries is confirmed to occur between the equivalent rigid–rigid and free–free cases.