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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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.
|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.|
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|Deposited On:||18 Sep 2007|
|Last Modified:||26 Dec 2012 09:42|
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