Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917733172510720 |
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| author | Zelati, Michele Coti Navarro-Fernández, Víctor |
| author_facet | Zelati, Michele Coti Navarro-Fernández, Víctor |
| contents | In this work we consider the Lagrangian properties of a random version of the Arnold-Beltrami-Childress (ABC) in a three-dimensional periodic box. We prove that the associated flow map possesses a positive top Lyapunov exponent and its associated one-point, two-point and projective Markov chains are geometrically ergodic. For a passive scalar, it follows that such a velocity is a space-time smooth exponentially mixing field, uniformly in the diffusivity coefficient. For a passive vector, it provides an example of a universal ideal (i.e. non-diffusive) kinematic dynamo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows Zelati, Michele Coti Navarro-Fernández, Víctor Analysis of PDEs Dynamical Systems Probability In this work we consider the Lagrangian properties of a random version of the Arnold-Beltrami-Childress (ABC) in a three-dimensional periodic box. We prove that the associated flow map possesses a positive top Lyapunov exponent and its associated one-point, two-point and projective Markov chains are geometrically ergodic. For a passive scalar, it follows that such a velocity is a space-time smooth exponentially mixing field, uniformly in the diffusivity coefficient. For a passive vector, it provides an example of a universal ideal (i.e. non-diffusive) kinematic dynamo. |
| title | Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows |
| topic | Analysis of PDEs Dynamical Systems Probability |
| url | https://arxiv.org/abs/2407.18028 |