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Modulation Theory Solution for Resonant Flow Over Topography

Smyth, N. F. (1987) Modulation Theory Solution for Resonant Flow Over Topography. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 409 (1836). pp. 79-97. ISSN 1364-5021. doi:10.2307/2398196.

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The near-resonant flow of a stratified fluid over topography is considered in the weakly nonlinear, long-wave limit, this flow being governed by a forced Korteweg-de Vries equation. It is proved from the modulation equations for the Korteweg-de Vries equation, which apply away from the obstacle, that no steady state can form upstream of the obstacle. This has been noted from previous experimental and numerical studies. The solution upstream and downstream of the topography is constructed as a simple wave solution of the modulation equations. Based on similarities between the method by which this solution is found and the quarter plane problem for the Korteweg-de Vries equation, the solution to the quarter plane problem is found for the special case in which a positive constant is specified at x = 0.

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Additional Information:© 1987 The Royal Society. Received 21 February 1986. The author wishes to thank Professor G. B. Whitham for his interest in the present work and for making possible a very enjoyable and profitable visit to Caltech. This research was supported by the Office of Naval Research.
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Issue or Number:1836
Record Number:CaltechAUTHORS:20150127-092210585
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Official Citation:Smyth, N. F. (1987). Modulation Theory Solution for Resonant Flow Over Topography. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 409(1836), 79-97. doi: 10.2307/2398196
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54129
Deposited On:27 Jan 2015 18:47
Last Modified:10 Nov 2021 20:29

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