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New exact relations for easy recovery of steady wave profiles from bottom pressure measurements

Published online by Cambridge University Press:  11 June 2013

Didier Clamond
Didier Clamond*
Affiliation:
Laboratoire J. A. Dieudonné, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice CEDEX 2, France
*
†Email address for correspondence: didierc@unice.fr
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Abstract

This paper is about the determination of a free surface wave profile from a given pressure distribution at the bottom. For a two-dimensional irrotational steady surface water wave propagating over a flat horizontal bed, this problem is solved analytically in an implicit form. Explicit solutions can be easily obtained numerically via fixed point iterations, whose convergence is outlined mathematically and numerically. This new surface reconstruction procedure does not involve the resolution of a differential or an integral equation, i.e. the surface is given by algebraic local relations. Thus, this formulation permits the free surface recovery in a simpler and more efficient way than previous methods.

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 726 , 10 July 2013 , pp. 547 - 558
Copyright
©2013 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Bishop, C. T. & Donelan, M. A. 1987 Measuring waves with pressure transducers. Coast. Engng 11, 309–328.Google Scholar
Clamond, D. 1999 Steady finite amplitude waves on a horizontal seabed of arbitrary depth. J. Fluid Mech. 398, 45–60.Google Scholar
Clamond, D. 2003 Cnoidal-type surface waves in deep water. J. Fluid Mech. 489, 101–120.Google Scholar
Clamond, D. & Constantin, A. 2013 Recovery of steady periodic wave profiles from pressure measurements at the bed. J. Fluid Mech. 714, 463–475.CrossRefGoogle Scholar
Clamond, D. & Fructus, D. 2003 Accurate simple approximation for the solitary wave. C. R. Mécanique 331, 727–732.CrossRefGoogle Scholar
Constantin, A. 2006 The trajectories of particles in Stokes waves. Invent. Math. 166, 523–535.Google Scholar
Constantin, A. 2012 On the recovery of solitary wave profiles from pressure measurements. J. Fluid Mech. 699, 373–384.CrossRefGoogle Scholar
Constantin, A. & Strauss, W. 2010 Pressure beneath a Stokes wave. Commun. Pure Appl. Maths 63, 533–557.Google Scholar
Deconinck, B., Oliveras, K. L. & Vasan, V. 2012 Relating the bottom pressure and the surface elevation in the water wave problem. J. Nonlinear Math. Phys. 19 (1), 1240014.Google Scholar
Devaney, R. L. 1989 An Introduction to Chaotic Dynamical Systems, 2nd edn. Addison-Wesley.Google Scholar
Escher, J. & Schlurmann, T. 2008 On the recovery of the free surface from the pressure within periodic traveling water waves. J. Nonlinear Math. Phys. 15, 50–57.Google Scholar
Fenton, J. D. 1979 A high-order cnoidal wave theory. J. Fluid Mech. 94, 129–161.CrossRefGoogle Scholar
Fenton, J. D. 1988 The numerical solution of steady water wave problems. Comput. Geosci. 14 (3), 357–368.Google Scholar
Longuet-Higgins, M. S. 1975 Integral properties of periodic gravity waves of finite amplitude. Proc. R. Soc. Lond. A 342, 157–174.Google Scholar
Oliveras, K. L., Vasan, V., Deconinck, B. & Henderson, D. 2012 Recovering surface elevation from pressure data. SIAM J. Appl. Maths 72, 897–918.Google Scholar
Tsai, C. H., Huang, M. C., Young, F. J., Lin, Y. C. & Li, H. W. 2005 On the recovery of surface wave by pressure transfer function. Ocean Engng 32, 1247–1259.Google Scholar