Dynamics of convective states and transition to chaos in quasi-static magnetoconvection

In this work, the dynamics of flow states in two-dimensional (2D) quasistatic magnetoconvection under the influence of a strong vertical magnetic field are explored. Top and bottom plates are free-slip, isothermal and the lateral boundaries are periodic. The strong imposed magnetic field, characterized by the Chandrasekhar number (Q), is anti-parallel to gravity, and the Prandtl number (Pr) is set to unity. Different initial conditions lead to different final statistically stationary states, characterized by a different number of stable rolls and a different set of global transport properties. Furthermore, the behavior of the system to initial conditions is also observed to be vital for the transition pathway to chaos. At a fixed Q, upon increasing the Rayleigh number (Ra), a specific set of initial conditions is observed to lead to an atypical bifurcation sequence, in which the flow reverts back to the steady/quasi-steady state after going through the phases of quasi-periodicity and weak turbulence, finally leading to chaos after yet another intermediary unsteady state. Consistent with similar observations for non-magnetic plane layer convection, it is shown that this atypical behavior of the transition from quasi-periodic/weakly-turbulent states to a steady state is accompanied by a significant changes in the length scale of the flow and the relative contributions of the Ohmic and viscous dissipation.