Oscillatory instability and routes to chaos in Rayleigh-Bénard convection: Effect of external magnetic field

Abstract

We investigate oscillatory instability and routes to chaos in Rayleigh-Bénard convection of electrically conducting fluids in the presence of an 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 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. The bifurcation analysis of the low-dimensional model shows that the origin of different routes is associated with the bifurcation structure near the primary instability. These observations show a similarity with the previous results of convection experiments performed with mercury.