Zero Prandtl-number rotating magnetoconvection

We investigate instabilities and chaos near the onset of Rayleigh-Bénard convection of electrically conducting fluids with free-slip, perfectly electrically and thermally conducting boundary conditions in the presence of uniform rotation about the vertical axis and horizontal external magnetic field by considering zero Prandtl-number limit (Pr → 0). Direct numerical simulations (DNSs) and low-dimensional modeling of the system are done for the investigation. Values of the Chandrasekhar number (Q) and the Taylor number (Ta) are varied in the range 0 < Q, Ta ≤ 50. Depending on the values of the parameters in the chosen range and the choice of initial conditions, the onset of convection is found be either periodic or chaotic. Interestingly, it is found that chaos at the onset can occur through four different routes, namely, homoclinic, intermittent, period doubling, and quasiperiodic routes. Homoclinic and intermittent routes to chaos at the onset occur in the presence of weak magnetic field (Q < 2), while the period doubling route is observed for relatively stronger magnetic field (Q ≥ 2) for one set of initial conditions. On the other hand, the quasiperiodic route to chaos at the onset is observed for another set of initial conditions. However, the rotation rate (value of Ta) also plays an important role in determining the nature of convection at the onset. Analysis of the system simultaneously with DNSs and low-dimensional modeling helps us to clearly identify different flow regimes concentrated near the onset of convection and understand their origins. The periodic or chaotic convection at the onset is found to be connected with rich bifurcation structures involving subcritical pitchfork, imperfect pitchfork, supercritical Hopf, imperfect homoclinic gluing, and Neimark-Sacker bifurcations.