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Modulational stability of cellular flows

Novikov, Alexei (2003) Modulational stability of cellular flows. Nonlinearity, 16 (5). pp. 1607-1639. ISSN 0951-7715. http://resolver.caltech.edu/CaltechAUTHORS:NOVnonlin03

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Abstract

We present here the homogenization of the equations for the initial modulational (large-scale) perturbations of stationary solutions of the two-dimensional Navier–Stokes equations with a time-independent periodic rapidly oscillating forcing. The stationary solutions are cellular flows and they are determined by the stream function phi = sinx1/epsilonsinx2/epsilon+δ cosx1/epsiloncosx2/epsilon, 0 ≤ δ ≤ 1. Two results are given here. For any Reynolds number we prove the homogenization of the linearized equations. For small Reynolds number we prove the homogenization for the fully nonlinear problem. These results show that the modulational stability of cellular flows is determined by the stability of the effective (homogenized) equations.


Item Type:Article
Additional Information:Copyright © Institute of Physics and IOP Publishing Limited 2007. Received 8 October 2002. Published 8 July 2003. Print publication: Issue 5 (September 2003). We are grateful to G Papanicolaou, L Berlyand and J Mattingly for reading a draft of this paper and making remarks about it.
Record Number:CaltechAUTHORS:NOVnonlin03
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:NOVnonlin03
Alternative URL:http://dx.doi.org/10.1088/0951-7715/16/5/304
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8809
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Sep 2007
Last Modified:26 Dec 2012 09:42

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