Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem
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| Format: | Preprint |
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2022
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| author | Laakmann, Fabian Boullé, Nicolas |
| author_facet | Laakmann, Fabian Boullé, Nicolas |
| contents | We perform a 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 $0\leq \Ra\leq 10^5$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_12163 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem Laakmann, Fabian Boullé, Nicolas Fluid Dynamics Numerical Analysis Computational Physics We perform a 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 $0\leq \Ra\leq 10^5$. 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. |
| title | Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem |
| topic | Fluid Dynamics Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2211.12163 |