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Averaging Versus Chaos in Turbulent Transport?

Owhadi, Houman (2004) Averaging Versus Chaos in Turbulent Transport? Communications in Mathematical Physics, 247 (3). pp. 553-599. ISSN 0010-3616. https://resolver.caltech.edu/CaltechAUTHORS:20160224-131618930

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Abstract

In this paper we analyze the transport of passive tracers by deterministic stationary incompressible flows which can be decomposed over an infinite number of spatial scales without separation between them. It appears that a low order dynamical system related to local Peclet numbers can be extracted from these flows and it controls their transport properties. Its analysis shows that these flows are strongly self-averaging and super-diffusive: the delay τ (r) for any finite number of passive tracers initially close to separate till a distance r is almost surely anomalously fast (τ (r)∼ r^(2–ν) , with ν > 0). This strong self-averaging property is such that the dissipative power of the flow compensates its convective power at every scale. However as the circulation increases in the eddies the transport behavior of the flow may (discontinuously) bifurcate and become ruled by deterministic chaos: the self-averaging property collapses and advection dominates dissipation. When the flow is anisotropic a new formula describing turbulent conductivity is identified.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00220-004-1069-8DOIArticle
http://link.springer.com/article/10.1007%2Fs00220-004-1069-8PublisherArticle
http://arxiv.org/abs/math-ph/0402028v1arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Additional Information:© 2004 Springer-Verlag. Received: 18 October 2002. Accepted: 15 November 2003. Communicated by A. Kupiainen. Part of this work was supported by the Aly Kaufman fellowship. The author would like to thank F. Castell, Y. Velenik and G. Ben Arous for reading the manuscript and A. Majda, T. Hou and P.E. Dimotakis for useful discussions.
Funders:
Funding AgencyGrant Number
Aly Kaufman fellowshipUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20160224-131618930
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160224-131618930
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64739
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 21:50
Last Modified:03 Oct 2019 09:40

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