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Abstract:
Quasistatic magnetoconvection of a fluid with low Prandtl number (Pr=0.025) with a vertical magnetic field is considered in a unit-aspect-ratio box with no-slip boundaries. At high relative magnetic field strengths, given by the Hartmann number Ha, the onset of convection is known to result from a sidewall instability giving rise to the wall-mode regime. Here, we carry out three-dimensional direct numerical simulations of unprecedented length to map out the parameter space at Ha=200,500,1000, varying the Rayleigh number (Ra) over the range 6×105≲Ra≲5×108. We track the development of stable equilibria produced by this primary instability, identifying bifurcations leading to limit cycles and eventually to chaotic dynamics. At Ha=200, the steady wall-mode solution undergoes a symmetry-breaking bifurcation producing a state that features a coexistence between wall modes and a large-scale roll in the centre of the domain, which persists to higher Ra. However, under a stronger magnetic field at Ha=1000, the steady wall-mode solution undergoes a Hopf bifurcation producing a limit cycle which further develops to solutions that shadow an orbit homoclinic to a saddle point. Upon a further increase in Ra, the system undergoes a subsequent symmetry break producing a coexistence between wall modes and a large-scale roll, although the large-scale roll exists only for a small range of Ra, and chaotic dynamics primarily arise from a mixture of chaotic wall-mode dynamics and arrays of cellular structures.
