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

Published online by Cambridge University Press:  24 April 2023

Didier Clamond*
Affiliation:
Université Côte d'Azur, CNRS UMR 7351, Laboratoire J. A. Dieudonneé, Parc Valrose, 06108 Nice CEDEX 2, France
Joris Labarbe
Affiliation:
Université Côte d'Azur, CNRS UMR 7351, Laboratoire J. A. Dieudonneé, Parc Valrose, 06108 Nice CEDEX 2, France
David Henry
Affiliation:
School of Mathematical Sciences, University College Cork, Cork, Ireland
*
Email address for correspondence: didier.clamond@univ-cotedazur.fr

Abstract

We derive equations relating the pressure at a flat seabed and the free-surface profile for steady gravity waves with constant vorticity. The resulting set of nonlinear equations enables the recovery of the free surface from pressure measurements at the bed. Furthermore, the flow vorticity (unknown a priori) is determined solely from the bottom pressure as part of the recovery method. This approach is applicable even in the presence of stagnation points and its efficiency is illustrated via numerical examples.

Type
JFM Rapids
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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