Recovering surface profiles of solitary waves on a uniform stream from pressure measurements

Hung-Chu Hsu

doi:10.3934/dcds.2014.34.3035

Article Contents

2014, Volume 34, Issue 8: 3035-3043. Doi: 10.3934/dcds.2014.34.3035

This issue Previous Article One-dimensional weakly nonlinear model equations for Rossby waves Next Article Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories

Recovering surface profiles of solitary waves on a uniform stream from pressure measurements

Hung-Chu Hsu^1,

1.
Department of Mathematics, King's College London, Strand, London WC2R 2LS

Received: March 31, 2013

Revised: August 31, 2013

Published: July 2014

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Abstract

In this paper, we derive an explicit formula that permits to recover the free surface wave profile of an irrotational solitary wave with a uniform underlying current from pressure data measured at the flat bed of the fluid. The formula is valid for the governing equations and applies to waves of small and large amplitude.

Keywords:

Pressure,
solitary wave,
current.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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