Chaotic advection in a steady three-dimensional MHD flow
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911247657598976 |
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| author | Fontchastagner, Julien Scheid, Jean-François Angilella, Jean-Régis Brancher, Jean-Pierre |
| author_facet | Fontchastagner, Julien Scheid, Jean-François Angilella, Jean-Régis Brancher, Jean-Pierre |
| contents | We investigate the 3D stationary flow of a weakly conducting fluid in a cubic cavity, driven by the Lorentz force created by two permanent magnets and a weak constant current. Our goal is to determine the conditions leading to efficient mixing within the cavity. The flow is composed of a large recirculation cell created by one side magnet, superposed to two recirculation cells created by a central magnet perpendicular to the first one. The overall structure of this flow, obtained here by solving the Stokes equations with Lorentz forcing, is similar to the tri-cellular model flow studied by Toussaint et. al. (Phys. Fluids. 7, 1995). Chaotic advection in this flow is analyzed by means of Poincaré sections, Lyapunov exponents and expansion entropies. In addition, we quantify the quality of mixing by computing contamination rates, homogeneity, as well as mixing times. Though individual vortices have poor mixing properties, the superposition of both flows creates chaotic streamlines and efficient mixing. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_20021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chaotic advection in a steady three-dimensional MHD flow Fontchastagner, Julien Scheid, Jean-François Angilella, Jean-Régis Brancher, Jean-Pierre Fluid Dynamics Chaotic Dynamics Computational Physics 76D07 (Primary) 76W05, 65M60 (Secondary) We investigate the 3D stationary flow of a weakly conducting fluid in a cubic cavity, driven by the Lorentz force created by two permanent magnets and a weak constant current. Our goal is to determine the conditions leading to efficient mixing within the cavity. The flow is composed of a large recirculation cell created by one side magnet, superposed to two recirculation cells created by a central magnet perpendicular to the first one. The overall structure of this flow, obtained here by solving the Stokes equations with Lorentz forcing, is similar to the tri-cellular model flow studied by Toussaint et. al. (Phys. Fluids. 7, 1995). Chaotic advection in this flow is analyzed by means of Poincaré sections, Lyapunov exponents and expansion entropies. In addition, we quantify the quality of mixing by computing contamination rates, homogeneity, as well as mixing times. Though individual vortices have poor mixing properties, the superposition of both flows creates chaotic streamlines and efficient mixing. |
| title | Chaotic advection in a steady three-dimensional MHD flow |
| topic | Fluid Dynamics Chaotic Dynamics Computational Physics 76D07 (Primary) 76W05, 65M60 (Secondary) |
| url | https://arxiv.org/abs/2405.20021 |