Low-dimensional dynamical system for Rayleigh-Bénard convection subjected to magnetic field

We have numerically investigated the dynamical behavior of Rayleigh-Benard (RB) convection in an incompressible conducting fluid subjected to a magnetic field by solving a low-dimensional dynamical system. Its dynamical properties are quantified by nonlinear time series analysis based on chaos theory. The stretching and folding in the phase space for the chaos region (normalized Rayleigh number r = 28) and the intermittent chaos region (r = 166.1) of RB convection at a high magnetic Prandtl number of Pm = 10 become complex with increasing applied magnetic field, and the degeneration of chaos is induced by the limit of the strong magnetic field owing to the overwhelming Lorentz force compared with the buoyancy. The results obtained in this study show the importance of the magnetic Prandtl number to the dynamical behavior of RB convection subjected to a magnetic field.

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