# Recovering the water-wave profile from pressure measurements

K. L. Oliveras, V. Vasan, B. Deconinck, D. Henderson

Research output: Contribution to journalArticle

43 Citations (Scopus)

### Abstract

A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the surface elevation which is obtained from the Euler formulation of the water-wave problem without approximation. From this new equation, a variety of different asymptotic formulas are derived. The nonlocal equation and the asymptotic formulas are compared with both numerical data and physical experiments. The solvability properties of the nonlocal equation are rigorously analyzed using the implicit function theorem.

Original language English (US) 897-918 22 SIAM Journal on Applied Mathematics 72 3 https://doi.org/10.1137/110853285 Published - Sep 7 2012

### Fingerprint

Nonlocal Equations
Water waves
Water Waves
Pressure measurement
Asymptotic Formula
Nonlinear equations
Implicit Function Theorem
Fluids
Solvability
Euler
Nonlinear Equations
Numerical Solution
Fluid
Formulation
Experiments
Approximation
Experiment
Profile

### All Science Journal Classification (ASJC) codes

• Applied Mathematics

### Cite this

Oliveras, K. L. ; Vasan, V. ; Deconinck, B. ; Henderson, D. / Recovering the water-wave profile from pressure measurements. In: SIAM Journal on Applied Mathematics. 2012 ; Vol. 72, No. 3. pp. 897-918.
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Recovering the water-wave profile from pressure measurements. / Oliveras, K. L.; Vasan, V.; Deconinck, B.; Henderson, D.

In: SIAM Journal on Applied Mathematics, Vol. 72, No. 3, 07.09.2012, p. 897-918.

Research output: Contribution to journalArticle

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