-We investigate oscillatory instability and routes to chaos in Rayleigh-Bénard convection of electrically conducting fluids in presence of external horizontal magnetic field. Three dimensional direct numerical simulations (DNS) of the governing equations are performed for the investigation. DNS shows that oscillatory instability is inhibited by the magnetic field. The supercritical Rayleigh number for the onset of oscillation is found to scale with the Chandrasekhar number Q as Q α in DNS with α = 1.8 for low Prandtl numbers (Pr). Most interestingly, DNS shows Q dependent routes to chaos for low Prandtl number fluids like mercury (Pr = 0.025). For low Q, period doubling routes are observed, while, quasiperiodic routes are observed for high Q. The bifurcation structure associated with Q dependent routes to chaos is then understood by constructing a low dimensional model from the DNS data. The model also shows similar scaling laws as DNS. Bifurcation analysis of the low dimensional model shows that origin of different routes are associated with the bifurcation structure near the primary instability. These observations show similarity with the previous results of convection experiments performed with mercury.
We investigate the transitions near the onset of thermal convection in electrically conducting low Prandtl-number (Pr) fluids in the presence of rotation about a vertical axis and external horizontal magnetic field. Three-dimensional direct numerical simulations (DNSs) and low dimensional modeling are performed with the Rayleigh–Bénard convection system in the ranges 0 < Q ≤ 1000 and 0 < Ta ≤ 500 of the Chandrasekhar number (Q) and the Taylor number (Ta), respectively, for that purpose. For larger Q(≥32.7), DNSs show substantial enhancement of convective heat transport and only finite amplitude steady two dimensional roll patterns at the onset. On the other hand, for smaller Q(<32.7), very rich dynamics involving different stationary as well as time dependent patterns, including stationary two-dimensional rolls, cross rolls, and oscillatory cross rolls, are observed at the onset of convection. Our investigation uncovers the cause of enhancement of heat transport and the origin of different flow patterns at the onset. We establish that a first order transition to convection occurring at the onset is responsible for the enhancement of the heat transport there. Furthermore, as the Rayleigh number (Ra) is increased beyond the onset, subsequent transitions near it are also explored in detail for smaller Q, and these are found to be associated with a variety of bifurcations including subcritical/supercritical pitchfork, Hopf, imperfect pitchfork, imperfect gluing, and Neimark–Sacker.
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