Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem
share
We perform bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem using a numerical technique called deflated continuation. Our aim is to study the influence of the magnetic field on the bifurcation diagram as the Chandrasekhar number Q increases, and compare it to the standard (non-magnetic) Rayleigh-Bénard problem. We compute steady states at a high Chandrasekhar number of Q=10^3 over a range of the Rayleigh number 0≤Ra≤ 10^5. These solutions are obtained by combining deflation with a continuation of steady states at low Chandrasekhar number, which allows us to explore the influence of the strength of the magnetic field as Q increases from low coupling, where the magnetic effect is almost negligible, to strong coupling at Q=10^3. We discover a large profusion of states with rich dynamics and observe a complex bifurcation structure with several pitchfork, Hopf and saddle-node bifurcations. Our numerical simulations show that the onset of bifurcations in the problem is delayed when Q increases, while solutions with fluid velocity patterns aligning with the background vertical magnetic field are privileged. Additionally, we report a branch of states that stabilizes at high magnetic coupling, suggesting that one may take advantage of the magnetic field to discriminate solutions.
READ FULL TEXT