Viscous perturbations of marginally stable Euler flow and finite-time Melnidov theory
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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. ISSN 0951-7715
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Abstract
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 |
|---|---|
| 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. |
| Uncontrolled Keywords: | Viscous perturbations, Euler flow, Finite-time Melinkov theory |
| Divisions: | Faculty of Engineering and Physical Sciences > Mathematics |
| ID Code: | 1475 |
| Deposited By: | Mr Adam Field |
| Deposited On: | 27 May 2010 15:41 |
| Last Modified: | 28 Sep 2012 10:50 |
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