Effects of a small magnetic field on homoclinic bifurcations in a low-Prandtl-number fluid.

Abstract

Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a fluid of Prandtl number Pr = 0.01 are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either in the vertical direction or in the horizontal direction. For a weak vertical magnetic field, the possibilities of both forward and backward homoclinic bifurcations are observed leading to a spontaneous gluing of two limit cycles into one as well as a spontaneous breaking of a limit cycle into two for lower values of the Chandrasekhar's number ( Q≤5). A slightly stronger magnetic field makes the convective flow time independent giving the possibility of stationary patterns at the secondary instability. For horizontal magnetic field, the x⇋y symmetry is destroyed and neither a homoclinic gluing nor a homoclinic breaking is observed. Two low-dimensional models are also constructed: one for a weak vertical magnetic field and another for a weak horizontal magnetic field. The models qualitatively capture the features observed in DNS and help understanding the unfolding of bifurcations close to the onset of magnetoconvection.