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Bounds for Arbitrary Steady Gravity Waves on Water of Finite Depth
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Russian Academy of Sciences.
2009 (English)In: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, Vol. 11, no 3, 325-347 p.Article in journal (Refereed) Published
Abstract [en]

  Necessary conditions for the existence of arbitrary bounded steady waves are proved (earlier, these conditions, that have the form of bounds on the Bernoulli constant and other wave characteristics, were established only for Stokes waves). It is also shown that there exists an exact upper bound such that if the free-surface profile is less than this bound at infinity (positive, negative, or both), then the profile asymptotes the constant level corresponding to a unform stream (supercritical or subcritical). Finally, an integral property of arbitrary steady waves is obtained. A new technique is proposed for proving these results; it is based on modified Bernoulli’s equation that along with the free surface profile involves the difference between the potential and its vertical average.

Place, publisher, year, edition, pages
2009. Vol. 11, no 3, 325-347 p.
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URN: urn:nbn:se:liu:diva-41018DOI: 10.1007/s00021-007-0261-yLocal ID: 54935OAI: diva2:261868
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2009-11-04

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Kozlov, Vladimir
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