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Recovery of steady periodic wave profiles from pressure measurements at the bed

Published online by Cambridge University Press:  02 January 2013

D. Clamond  and
A. Constantin
D. Clamond
Affiliation:
Laboratoire J.-A. Dieudonné, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice CEDEX 2, France
A. Constantin*
Affiliation:
Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria
*
†Email address for correspondence: [email protected]
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Abstract

We derive an equation relating the pressure at the flat bed and the profile of an irrotational steady water wave, valid for all classical solutions of the governing equations for water waves. This permits the recovery of the surface wave from pressure measurements at the bed. Although we focus on periodic waves, the extension to solitary waves is straightforward. We illustrate the usefulness of the equation beyond the realm of linear theory by investigating the regime of shallow-water waves of small amplitude and by presenting a numerical example.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 714 , 10 January 2013 , pp. 463 - 475
Copyright
©2013 Cambridge University Press

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