Effects of a small magnetic field on homoclinic bifurcations in a   low-Prandtl-number fluid
  Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-B\'{e}nard 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 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 merging 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 ($Q\leq 5$). 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 $x\leftrightharpoons y$ 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. 
Arnab Basak and Krishna Kumar
physics.flu-dyn