Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-25T19:41:30.162Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  24 April 2023

Didier Clamond Open the ORCID record for Didier Clamond [Opens in a new window] ,
Joris Labarbe Open the ORCID record for Joris Labarbe [Opens in a new window]  and
David Henry Open the ORCID record for David Henry [Opens in a new window]
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
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Mathematical Foundations: General fluid mechanics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 961 , 25 April 2023 , R2
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aris, R. 1962 Vectors, Tensors and Basic Equations of Fluid Mechanics. Dover.Google Scholar
Brink-Kjær, O. 1976 Gravity waves on a current: the influence of vorticity, a sloping bed, and dissipation. In Institute of Hydrodynamics and Hydraulic Engineering, (ISVA), vol. 12, pp. 1–137. Technical University of Denmark.Google Scholar
Clamond, D. 2013 New exact relations for easy recovery of steady wave profiles from bottom pressure measurements. J. Fluid Mech. 726, 547–558.CrossRefGoogle Scholar
Clamond, D. 2017 Remarks on Bernoulli constants, gauge conditions and phase velocities in the context of water waves. Appl. Maths Lett. 74, 114–120.CrossRefGoogle Scholar
Clamond, D. 2018 New exact relations for steady irrotational two-dimensional gravity and capillary surface waves. Phil. Trans. R. Soc. A 376 (2111), 20170220.Google ScholarPubMed
Clamond, D. & Barthélémy, E. 1995 Experimental determination of the phase shift in the Stokes wave – solitary wave interaction. C. R. Acad. Sci. Paris IIb 320 (6), 277–280.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. & Dutykh, D. 2018 Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth. J. Fluid Mech. 844, 491–518.Google Scholar
Clamond, D. & Henry, D. 2020 Extreme water-wave profile recovery from pressure measurements at the seabed. J. Fluid Mech. 903 (R3), 12.CrossRefGoogle Scholar
Constantin, A. 2011 Nonlinear Water Waves with Applications to Wave–Current Interactions and Tsunamis, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 81. SIAM.Google Scholar
Constantin, A. 2012 On the recovery of solitary wave profiles from pressure measurements. J. Fluid Mech. 699, 376–384.CrossRefGoogle Scholar
Constantin, A. 2016 Extrema of the dynamic pressure in an irrotational regular wave train. Phys. Fluids 28 (11), 113604.CrossRefGoogle Scholar
Constantin, A., Strauss, W. & Varvaruca, E. 2016 Global bifurcation of steady gravity water waves with critical layers. Acta Mathematica 217 (2), 195–262.Google Scholar
Constantin, A., Strauss, W. & Varvaruca, E. 2021 Large-amplitude steady downstream water waves. Commun. Math. Phys. 387 (1), 237–266.CrossRefGoogle Scholar
Constantin, A. & Varvaruca, E. 2011 Steady periodic water waves with constant vorticity: regularity and local bifurcation. Arch. Rat. Mech. Anal. 199 (1), 33–67.Google Scholar
Da Silva, A.T. & Peregrine, D.H. 1988 Steep, steady surface waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281–302.CrossRefGoogle Scholar
Henry, D. 2013 On the pressure transfer function for solitary water waves with vorticity. Math. Ann. 357 (1), 23–30.Google Scholar
Henry, D. & Thomas, G.P. 2018 Prediction of the free-surface elevation for rotational water waves using the recovery of pressure at the bed. Phil. Trans. R. Soc. A 376 (2111), 20170102, 21.Google ScholarPubMed
Kishida, N. & Sobey, J. 1988 Stokes theory for waves on linear shear current. J. Engng Mech. ASCE 114 (8), 1317–1334.Google Scholar
Okamoto, H. & Shoji, M. 2001 The Mathematical Theory of Permanent Progressive Water-Waves, Advanced Series in Nonlinear Dynamics, vol. 20. World Scientific Publishing Co., Inc.CrossRefGoogle Scholar
Oliveras, K.L., Vasan, V., Deconinck, B. & Henderson, D. 2012 Recovering the water-wave profile from pressure measurements. SIAM J. Appl. Maths 72 (3), 897–918.CrossRefGoogle Scholar
Thomas, G.P. & Klopman, G. 1997 Wave–current interactions in the nearshore region. In Gravity Waves in Water of Finite Depth (ed. J.N. Hunt), Advances in Fluid Mechanics, pp. 255–319. Computational Mechanics Publications.Google Scholar