| Searching for the fastest dynamo: Laminar ABC flows. | |
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MedLine Citation:
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PMID: 21929104 Owner: NLM Status: In-Data-Review |
Abstract/OtherAbstract:
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The growth rate of the dynamo instability as a function of the magnetic Reynolds number R_{_{M}} is investigated by means of numerical simulations for the family of the Arnold-Beltrami-Childress (ABC) flows and for two different forcing scales. For the ABC flows that are driven at the largest available length scale, it is found that, as the magnetic Reynolds number is increased: (a) The flow that results first in a dynamo is the 21/2-dimensional flow for which A=B and C=0 (and all permutations). (b) The second type of flow that results in a dynamo is the one for which A=B≃2C/5 (and permutations). (c) The most symmetric flow, A=B=C, is the third type of flow that results in a dynamo. (d) As R_{_{M}} is increased, the A=B=C flow stops being a dynamo and transitions from a local maximum to a third-order saddle point. (e) At larger R_{_{M}}, the A=B=C flow reestablishes itself as a dynamo but remains a saddle point. (f) At the largest examined R_{_{M}}, the growth rate of the 21/2-dimensional flows starts to decay, the A=B=C flow comes close to a local maximum again, and the flow A=B≃2C/5 (and permutations) results in the fastest dynamo with growth rate γ≃0.12 at the largest examined R_{_{M}}. For the ABC flows that are driven at the second largest available length scale, it is found that (a) the 21/2-dimensional flows A=B,C=0 (and permutations) are again the first flows that result in a dynamo with a decreased onset. (b) The most symmetric flow, A=B=C, is the second type of flow that results in a dynamo. It is, and it remains, a local maximum. (c) At larger R_{M}, the flow A=B≃2C/5 (and permutations) appears as the third type of flow that results in a dynamo. As R_{_{M}} is increased, it becomes the flow with the largest growth rate. The growth rates appear to have some correlation with the Lyapunov exponents, but constructive refolding of the field lines appears equally important in determining the fastest dynamo flow. |
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Authors:
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Alexandros Alexakis |
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Publication Detail:
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Type: Journal Article Date: 2011-08-18 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 84 ISSN: 1550-2376 ISO Abbreviation: Phys Rev E Stat Nonlin Soft Matter Phys Publication Date: 2011 Aug |
Date Detail:
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Created Date: 2011-09-20 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: United States |
Other Details:
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Languages: eng Pagination: 026321 Citation Subset: IM |
Affiliation:
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Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, UMR CNRS 8550, 24 Rue Lhomond, F-75006 Paris Cedex 05, France. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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