Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-15T14:18:30.814Z Has data issue: false hasContentIssue false
  • English
  • Français

Surfing surface gravity waves

Published online by Cambridge University Press:  16 June 2017

Nick E. Pizzo Open the ORCID record for Nick E. Pizzo [Opens in a new window]
Nick E. Pizzo*
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0213, USA
*
†Email address for correspondence: npizzo@ucsd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497–503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 316 - 328
Check for updates
Copyright
© 2017 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

Baker, G. R. & Xie, C. 2011 Singularities in the complex physical plane for deep water waves. J. Fluid Mech. 685, 83–116.Google Scholar
Balk, A. M. 1996 A Lagrangian for water waves. Phys. Fluids 8 (2), 416–420.Google Scholar
Battjes, J. A. 1988 Surf-zone dynamics. Annu. Rev. Fluid Mech. 20 (1), 257–291.CrossRefGoogle Scholar
Bresnahan, P. J., Wirth, T., Martz, T. R., Andersson, A. J., Cyronak, T., DAngelo, S., Pennise, J., Melville, W. K., Lenain, L. & Statom, N. 2016 A sensor package for mapping ph and oxygen from mobile platforms. Meth. Oceanogr. 17, 1–13.CrossRefGoogle Scholar
Clark, D. B., Feddersen, F. & Guza, R. T. 2010 Cross-shore surfzone tracer dispersion in an alongshore current. J. Geophys. Res. 115, C10.Google Scholar
Craik, A. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73 (03), 401–426.Google Scholar
Dally, W. R. 2001 The maximum speed of surfers. J. Coast. Res. Special issue 29 33–40.Google Scholar
Dawson, J. 1961 On Landau damping. Phys. Fluids 4 (7), 869–874.CrossRefGoogle Scholar
Deike, L., Pizzo, N. E. & Melville, W. K. 2017 Lagrangian transport by breaking surface waves. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Deike, L., Popinet, S. & Melville, W. K. 2015 Capillary effects on wave breaking. J. Fluid Mech. 769, 541–569.CrossRefGoogle Scholar
Dold, J. W. 1992 An efficient surface-integral algorithm applied to unsteady gravity waves. J. Comput. Phys. 103 (1), 90–115.Google Scholar
Dold, J. W. & Peregrine, D. H. 1986 Water-wave modulation. Coast. Engng Proc. 1 (20), 163–175.Google Scholar
Drazen, D. A., Melville, W. K. & Lenain, L. 2008 Inertial scaling of dissipation in unsteady breaking waves. J. Fluid Mech. 611, 307–332.CrossRefGoogle Scholar
Feddersen, F. 2007 Breaking wave induced cross-shore tracer dispersion in the surf zone: model results and scalings. J. Geophys. Res. 112, C9.Google Scholar
Feddersen, F., Olabarrieta, M., Guza, R. T., Winters, D., Raubenheimer, B. & Elgar, S. 2016 Observations and modeling of a tidal inlet dye tracer plume. J. Geophys. Res 121, 7819–7844.CrossRefGoogle Scholar
Fedele, F. 2014 Geometric phases of water waves. Europhys. Lett. 107 (6), 69001.Google Scholar
Fedele, F., Chandre, C. & Farazmand, M. 2016 Kinematics of fluid particles on the sea surface. Part 1. Hamiltonian theory. J. Fluid Mech. 801, 260–288.Google Scholar
Inman, D. L., Tait, R. J. & Nordstrom, C. E. 1971 Mixing in the surf zone. J. Geophys. Res. 76 (15), 3493–3514.CrossRefGoogle Scholar
John, F. 1953 Two-dimensional potential flows with a free boundary. Commun. Pure Appl. Maths 6, 497–503.CrossRefGoogle Scholar
Landau, L. D. 1946 On the vibrations of the electronic plasma. Zh. Eksp. Teor. Fiz. 10, 25–34.Google Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15 (1), 391–427.Google Scholar
Longuet-Higgins, M. S. 1957 The statistical analysis of a random, moving surface. Phil. Trans. R. Soc. Lond. A 249 (966), 321–387.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
Longuet-Higgins, M. S. 1978a The instabilities of gravity waves of finite amplitude in deep water. I. Superharmonics. Proc. R. Soc. Lond. A 360 (1703), 471–488.Google Scholar
Longuet-Higgins, M. S. 1978b Some new relations between Stokes’s coefficients in the theory of gravity waves. IMA J. Appl. Maths 22 (3), 261–273.Google Scholar
Longuet-Higgins, M. S. 1980 A technique for time-dependent free-surface flows. Proc. R. Soc. Lond. A 371 (1747), 441–451.Google Scholar
Longuet-Higgins, M. S. 1982 Parametric solutions for breaking waves. J. Fluid Mech. 121, 403–424.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1985 Bifurcation in gravity waves. J. Fluid Mech. 151, 457–475.Google Scholar
Longuet-Higgins, M. S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659–679.Google Scholar
Longuet-Higgins, M. S. & Dommermuth, D. G. 1997 Crest instabilities of gravity waves. Part 3. Nonlinear development and breaking. J. Fluid Mech. 336, 33–50.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stresses in water waves; a physical discussion, with applications. Deep-Sea Res. Oceanogr. Abstracts 11 (4), 529–562.Google Scholar
McWilliams, J. C. & Restrepo, J. M. 1999 The wave-driven ocean circulation. J. Phys. Oceanogr. 29 (10), 2523–2540.Google Scholar
McWilliams, J. C., Restrepo, J. M. & Lane, E. M. 2004 An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech. 511, 135–178.CrossRefGoogle Scholar
Meiron, D. I., Orszag, S. A. & Israeli, M. 1981 Applications of numerical conformal mapping. J. Comput. Phys. 40 (2), 345–360.CrossRefGoogle Scholar
Melville, W. K., Veron, F. & White, C. J. 2002 The velocity field under breaking waves: coherent structure and turbulence. J. Fluid Mech. 454, 203–233.CrossRefGoogle Scholar
Mouhot, C. & Villani, C. 2010 Landau damping. J. Math. Phys. 51 (1), 015204.Google Scholar
Peregrine, D. H. 1983 Breaking waves on beaches. Annu. Rev. Fluid Mech. 15 (1), 149–178.Google Scholar
Perlin, M., Choi, W. & Tian, Z. 2013 Breaking waves in deep and intermediate waters. Annu. Rev. Fluid Mech. 45, 115–145.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Pizzo, N. E.2015 Properties of nonlinear and breaking deep-water surface waves. Doctoral thesis. University of California, San Diego.Google Scholar
Pizzo, N. E. & Melville, W. K. 2013 Vortex generation by deep-water breaking waves. J. Fluid Mech. 734, 198–218.CrossRefGoogle Scholar
Pizzo, N. E. & Melville, W. K.2017 A Lagrangian for water waves with application to the stability of stokes waves. (In preparation).Google Scholar
Pizzo, N. E., Melville, W. K. & Deike, L. 2016 Current generation by deep-water wave breaking. J. Fluid Mech. 803, 292–312.Google Scholar
Rapp, R. J. & Melville, W. K. 1990 Laboratory measurements of deep-water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735–800.Google Scholar
Romero, L., Melville, W. K. & Kleiss, J. M. 2012 Spectral energy dissipation due to surface wave breaking. J. Phys. Oceanogr. 42 (9), 1421–1444.Google Scholar
Sclavounos, P. D. 2005 Nonlinear particle kinematics of ocean waves. J. Fluid Mech. 540, 133–142.Google Scholar
Sinnett, G. & Feddersen, F. 2014 The surf zone heat budget: the effect of wave heating. Geophys. Res. Lett. 41 (20), 7217–7226.Google Scholar
Smith, J. A. 2006 Observed variability of ocean wave Stokes drift, and the Eulerian response to passing groups. J. Phys. Oceanogr. 36 (7), 1381–1402.Google Scholar
Sullivan, P. P., McWilliams, J. C. & Melville, W. K. 2004 The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations. J. Fluid Mech. 507, 143–174.Google Scholar
Sullivan, P. P., McWilliams, J. C. & Melville, W. K. 2007 Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers. J. Fluid Mech. 593, 405–452.Google Scholar
Tanaka, M. 1983 The stability of steep gravity waves. J. Phys. Soc. Japan 52 (9), 3047–3055.Google Scholar
Tanaka, M., Dold, J. W., Lewy, M. & Peregrine, D. H. 1987 Instability and breaking of a solitary wave. J. Fluid Mech. 185, 235–248.Google Scholar
Vinje, T. & Brevig, P. 1981 Numerical simulation of breaking waves. Adv. Water Resour. 4 (2), 77–82.CrossRefGoogle Scholar