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Viscous perturbations of marginally stable Euler flow and finite-time Melnidov theory

Grenier, Emmanuel, Jones, Christopher K. R. T., Rousset, Frederic and Sandstede, Björn (2004) Viscous perturbations of marginally stable Euler flow and finite-time Melnidov theory Nonlinearity, 18 (2). pp. 465-483.


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The effect of small viscous dissipation on Lagrangian transport in two-dimensional vorticity conserving fluid flows motivates this work. If the inviscid equation admits a base flow in which different fluid regions are divided by separatrices, then transport between these regions is afforded by the splitting of separatrices caused by viscous dissipation. Finite-time Melnikov theory allows us to measure the splitting distance of separatrices provided the perturbed velocity field of the viscous fluid flow stays sufficiently close to vorticity-conserving base flow over sufficiently long time intervals. In this paper, we derive the necessary long-term estimates of solutions to Euler’s equation and to the barotropic vorticity equation upon adding viscous perturbations and forcing. We discover that a certain stability condition on the unperturbed flow is sufficient to guarantee these long time estimates.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Grenier, Emmanuel
Jones, Christopher K. R. T.
Rousset, Frederic
Sandstede, Bjö
Date : 25 November 2004
DOI : 10.1088/0951-7715/18/2/001
Uncontrolled Keywords : Viscous perturbations, Euler flow, Finite-time Melinkov theory
Additional Information : This is a pre-copy-editing, author-prepared, peer-reviewed PDF of an article published in Nonlinearity, 18, 465-483. © 2005 Publishing Ltd and London Mathematical Society. Click here to access the publisher's version.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 31 Oct 2017 14:02

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