Shklyaev, S. and Khenner, M. and Alabuzhev, A. A. (2010) Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film. Physical Review E, 82 (2). Art. No. 025302 . ISSN 1539-3755 http://resolver.caltech.edu/CaltechAUTHORS:20100831-100707824
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Abstract
We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O(√Bi), where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.
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| Additional Information: | © 2010 The American Physical Society. Received 18 February 2010; revised manuscript received 20 April 2010; published 12 August 2010. We are grateful to A. A. Nepomnyashchy and A. Oron for the fruitful discussions. S.S. and A.A.A. are partially supported by joint grants of the Israel Ministry of Sciences (Grant No. 3-5799) and Russian Foundation for Basic Research (Grant No. 09-01-92472). M.K. acknowledges the support of WKU Faculty Scholarship Council via Grants No. 10-7016 and No. 10-7054. | ||||||||||
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| Classification Code: | PACS: 47.15.gm, 47.20.Ky, 47.55.pf, 68.08.Bc | ||||||||||
| Record Number: | CaltechAUTHORS:20100831-100707824 | ||||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20100831-100707824 | ||||||||||
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 19736 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | Tony Diaz | ||||||||||
| Deposited On: | 01 Sep 2010 18:38 | ||||||||||
| Last Modified: | 26 Dec 2012 12:22 |
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