Sharp-Crested Breaking Surface Waves Observed from a Ship-Based Stereo Video System

Michael S. Schwendeman Applied Physics Laboratory, University of Washington, Seattle, Washington

Search for other papers by Michael S. Schwendeman in
Current site
Google Scholar
PubMed
Close
and
Jim Thomson Applied Physics Laboratory, University of Washington, Seattle, Washington

Search for other papers by Jim Thomson in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A new ship-based stereo video system is used to observe breaking ocean waves (i.e., whitecaps) as three-dimensional surfaces evolving in time. First, the stereo video measurements of all waves (breaking and nonbreaking) are shown to compare well with statistical parameters from traditional buoy measurements. Next, the breaking waves are detected based on the presence of whitecap foam, and the geometry of these waves is investigated. The stereo measurements show that the whitecaps are characterized by local extremes of surface slope, though the larger-scale, crest-to-trough steepness of these waves is unremarkable. Examination of 103 breaking wave profiles further demonstrates the pronounced increase in the local wave steepness near the breaking crest, as estimated using a Hilbert transform. These crests are found to closely resemble the sharp corner of the theoretical Stokes limiting wave. Results suggest that nonlinear wave group dynamics are a key mechanism for breaking, as the phase speed of the breaking waves is slower than predicted by the linear dispersion relation. The highly localized and transient steepness, along with the deviation from linear phase speed, explains the inability of conventional wave buoys to observe the detailed geometry of breaking waves.

Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JPO-D-16-0187.s1.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Michael S. Schwendeman, mss28@u.washington.edu

Abstract

A new ship-based stereo video system is used to observe breaking ocean waves (i.e., whitecaps) as three-dimensional surfaces evolving in time. First, the stereo video measurements of all waves (breaking and nonbreaking) are shown to compare well with statistical parameters from traditional buoy measurements. Next, the breaking waves are detected based on the presence of whitecap foam, and the geometry of these waves is investigated. The stereo measurements show that the whitecaps are characterized by local extremes of surface slope, though the larger-scale, crest-to-trough steepness of these waves is unremarkable. Examination of 103 breaking wave profiles further demonstrates the pronounced increase in the local wave steepness near the breaking crest, as estimated using a Hilbert transform. These crests are found to closely resemble the sharp corner of the theoretical Stokes limiting wave. Results suggest that nonlinear wave group dynamics are a key mechanism for breaking, as the phase speed of the breaking waves is slower than predicted by the linear dispersion relation. The highly localized and transient steepness, along with the deviation from linear phase speed, explains the inability of conventional wave buoys to observe the detailed geometry of breaking waves.

Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JPO-D-16-0187.s1.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Michael S. Schwendeman, mss28@u.washington.edu

Supplementary Materials

    • Supplemental Materials (MP4 659 KB)
Save
  • Babanin, A., 2011: Breaking and Dissipation of Ocean Surface Waves. Cambridge University Press, 463 pp.

  • Babanin, A., D. Chalikov, I. Young, and I. Savelyev, 2007: Predicting the breaking onset of surface water waves. Geophys. Res. Lett., 34, L07605, doi:10.1029/2006GL029135.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Babanin, A., D. Chalikov, I. R. Young, and I. Savelyev, 2010: Numerical and laboratory investigation of breaking of steep two-dimensional waves in deep water. J. Fluid Mech., 644, 433463, doi:10.1017/S002211200999245X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Banner, M. L., 1990: Equilibrium spectra of wind waves. J. Phys. Oceanogr., 20, 966984, doi:10.1175/1520-0485(1990)020<0966:ESOWW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Banner, M. L., and W. L. Pierson, 2007: Wave breaking onset and strength for two-dimensional deep water wave groups. J. Fluid Mech., 585, 93115, doi:10.1017/S0022112007006568.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Banner, M. L., A. V. Babanin, and I. Young, 2000: Breaking probability for dominant waves on the sea surface. J. Phys. Oceanogr., 30, 31453160, doi:10.1175/1520-0485(2000)030<3145:BPFDWO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Banner, M. L., X. Barthelemy, F. Fedele, M. Allis, A. Benetazzo, F. Dias, and W. L. Pierson, 2014: Linking reduced breaking crest speeds to unsteady nonlinear water wave group behavior. Phys. Rev. Lett., 112, 114502, doi:10.1103/PhysRevLett.112.114502.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benetazzo, A., 2006: Measurements of short water waves using stereo matched image sequences. Coastal Eng., 53, 10131032, doi:10.1016/j.coastaleng.2006.06.012.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benetazzo, A., F. Fedele, G. Gallego, P.-C. Shih, and A. Yezzi, 2012: Offshore stereo measurements of gravity waves. Coastal Eng., 64, 127138, doi:10.1016/j.coastaleng.2012.01.007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benetazzo, A., F. Barbariol, F. Bergamasco, A. Torsello, S. Carniel, and M. Sclavo, 2015: Observation of extreme sea waves in a space–time ensemble. J. Phys. Oceanogr., 45, 22612275, doi:10.1175/JPO-D-15-0017.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benetazzo, A., F. Barbariol, F. Bergamasco, A. Torsello, S. Carniel, and M. Sclavo, 2016: Stereo wave imaging from moving vessels: Practical use and applications. Coastal Eng., 109, 114127, doi:10.1016/j.coastaleng.2015.12.008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, M. G., and A. Jensen, 2001: Experiments on focusing unidirectional water waves. J. Geophys. Res., 106, 16 91716 928, doi:10.1029/2000JC000584.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chalikov, D., 2005: Statistical properties of nonlinear one-dimensional wave fields. Nonlinear Processes Geophys., 12, 671689, doi:10.5194/npg-12-671-2005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chalikov, D., and A. V. Babanin, 2012: Simulation of wave breaking in one-dimensional spectral environment. J. Phys. Oceanogr., 42, 17451761, doi:10.1175/JPO-D-11-0128.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cox, C., and W. Munk, 1954: Measurement of the roughness of the sea surface from photographs of the sun’s glitter. J. Opt. Soc. Amer., 44, 838850, doi:10.1364/JOSA.44.000838.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • de Vries, J. J., 2014: Datawell Waverider reference manual: DWR-MkIII, DWR-G. Datawell BV Rep., 147 pp.

  • de Vries, S., D. F. Hill, M. A. de Schipper, and M. J. F. Stive, 2011: Remote sensing of surf zone waves using stereo imaging. Coastal Eng., 58, 239250, doi:10.1016/j.coastaleng.2010.10.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Drazen, D., W. K. Melville, and L. Lenain, 2008: Inertial scaling of dissipation in unsteady breaking waves. J. Fluid Mech., 611, 307332, doi:10.1017/S0022112008002826.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duncan, J. H., 1981: An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. Roy. Soc. London, A377, 331348, doi:10.1098/rspa.1981.0127.

    • Search Google Scholar
    • Export Citation
  • Fedele, F., A. Benetazzo, G. Gallego, P.-C. Shih, A. Yezzi, F. Barbariol, and F. Ardhuin, 2013: Space–time measurements of oceanic sea states. Ocean Modell., 70, 103115, doi:10.1016/j.ocemod.2013.01.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Forristall, G. Z., 2000: Wave crest distributions: Observations and second-order theory. J. Phys. Oceanogr., 30, 19311943, doi:10.1175/1520-0485(2000)030<1931:WCDOAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gemmrich, J. R., and D. Farmer, 1999: Observations of the scale and occurrence of breaking surface waves. J. Phys. Oceanogr., 29, 25952606, doi:10.1175/1520-0485(1999)029<2595:OOTSAO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gemmrich, J. R., M. L. Banner, and C. Garrett, 2008: Spectrally resolved energy dissipation rate and momentum flux of breaking waves. J. Phys. Oceanogr., 38, 12961312, doi:10.1175/2007JPO3762.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Herbers, T. H. C., and T. T. Janssen, 2016: Lagrangian surface wave motion and Stokes drift fluctuations. J. Phys. Oceanogr., 46, 10091021, doi:10.1175/JPO-D-15-0129.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Herbers, T. H. C., P. F. Jessen, T. T. Janssen, D. B. Colbert, and J. H. MacMahan, 2012: Observing ocean surface waves with GPS-tracked buoys. J. Atmos. Oceanic Technol., 29, 944959, doi:10.1175/JTECH-D-11-00128.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hirschmuller, H., 2008: Stereo processing by semi-global matching and mutual information. IEEE Trans. Pattern Anal. Mach. Intell., 30, 328341, doi:10.1109/TPAMI.2007.1166.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holthuijsen, L. H., 1983: Stereophotography of ocean waves. Appl. Ocean Res., 5, 204209, doi:10.1016/0141-1187(83)90034-2.

  • Holthuijsen, L. H., and T. H. C. Herbers, 1986: Statistics of breaking waves observed as whitecaps in the open sea. J. Phys. Oceanogr., 16, 290297, doi:10.1175/1520-0485(1986)016<0290:SOBWOA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jähne, B., J. Klinke, and S. Waas, 1994: Imaging of short ocean wind waves: A critical theoretical review. J. Opt. Soc. Amer., 11A, 21972209, doi:10.1364/JOSAA.11.002197.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kleiss, J. M., and W. K. Melville, 2011: The analysis of sea surface imagery for whitecap kinematics. J. Atmos. Oceanic Technol., 28, 219243, doi:10.1175/2010JTECHO744.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leckler, F., F. Ardhuin, C. Peureux, A. Benetazzo, F. Bergamasco, and V. Dulov, 2015: Analysis and interpretation of frequency–wavenumber spectra of young wind waves. J. Phys. Oceanogr., 45, 24842496, doi:10.1175/JPO-D-14-0237.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, P. C., and A. V. Babanin, 2004: Using wavelet spectrum analysis to resolve breaking events in the wind wave time series. Ann. Geophys., 22, 33353345, doi:10.5194/angeo-22-3335-2004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, Y., X.-H. Yan, W. T. Liu, and P. A. Hwang, 1997: The probability density function of ocean surface slopes and its effects on radar backscatter. J. Phys. Oceanogr., 27, 782797, doi:10.1175/1520-0485(1997)027<0782:TPDFOO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., 1963: The effect of non-linearities on statistical distributions in the theory of sea waves. J. Fluid Mech., 17, 459480, doi:10.1017/S0022112063001452.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Melville, W. K., 1996: The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech., 28, 279321, doi:10.1146/annurev.fl.28.010196.001431.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Perlin, M., W. Choi, and Z. Tian, 2013: Breaking waves in deep and intermediate waters. Annu. Rev. Fluid Mech., 45, 115145, doi:10.1146/annurev-fluid-011212-140721.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Phillips, O. M., 1985: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech., 156, 505531, doi:10.1017/S0022112085002221.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rainey, R. C. T., and M. S. Longuet-Higgins, 2006: A close one-term approximation to the highest Stokes wave on deep water. Ocean Eng., 33, 20122024, doi:10.1016/j.oceaneng.2005.09.014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rapp, R. J., and W. K. Melville, 1990: Laboratory measurements of deep-water breaking waves. Philos. Trans. Roy. Soc. London, A331, 735800, doi:10.1098/rsta.1990.0098.

    • Search Google Scholar
    • Export Citation
  • Schwendeman, M., and J. Thomson, 2015a: A horizon-tracking method for shipboard video stabilization and rectification. J. Atmos. Oceanic Technol., 32, 164176, doi:10.1175/JTECH-D-14-00047.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schwendeman, M., and J. Thomson, 2015b: Observations of whitecap coverage and the relation to wind stress, wave slope, and turbulent dissipation. J. Geophys. Res. Oceans, 120, 83468363, doi:10.1002/2015JC011196.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Song, J., and M. L. Banner, 2002: On determining the onset and strength of breaking for deep water waves. Part I: Unforced irrotational wave groups. J. Phys. Oceanogr., 32, 25412558, doi:10.1175/1520-0485-32.9.2541.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stansell, P., and C. MacFarlane, 2002: Experimental investigation of wave breaking criteria based on wave phase speeds. J. Phys. Oceanogr., 32, 12691283, doi:10.1175/1520-0485(2002)032<1269:EIOWBC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stokes, G. G., 1880: On the theory of oscillatory waves. Mathematical and Physical Papers, Vol. 1, Cambridge University Press, 197–229, doi:10.1017/CBO9780511702242.013.

    • Crossref
    • Export Citation
  • Sutherland, P., and W. K. Melville, 2013: Field measurements and scaling of ocean surface wave-breaking statistics. Geophys. Res. Lett., 40, 30743079, doi:10.1002/grl.50584.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tayfun, M. A., 1986: On narrow-band representation of ocean waves: 1. Theory. J. Geophys. Res. Oceans, 91, 77437752, doi:10.1029/JC091iC06p07743.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomson, J., 2012: Wave breaking dissipation observed with ‘swift’ drifters. J. Atmos. Oceanic Technol., 29, 18661882, doi:10.1175/JTECH-D-12-00018.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomson, J., M. S. Schwendeman, S. F. Zippel, S. Moghimi, J. Gemmrich, and W. E. Rogers, 2016: Wave-breaking turbulence in the ocean surface layer. J. Phys. Oceanogr., 46, 18571870, doi:10.1175/JPO-D-15-0130.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tian, Z., M. Perlin, and W. Choi, 2010: Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model. J. Fluid Mech., 655, 217257, doi:10.1017/S0022112010000832.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tian, Z., M. Perlin, and W. Choi, 2012: An eddy viscosity model for two-dimensional breaking waves and its validation with laboratory experiments. Phys. Fluids, 24, 036601, doi:10.1063/1.3687508.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wanek, J. M., and C. H. Wu, 2006: Automated trinocular stereo imaging system for three-dimensional surface wave measurements. Ocean Eng., 33, 723747, doi:10.1016/j.oceaneng.2005.05.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weissman, M. A., S. S. Ataktürk, and K. B. Katsaros, 1984: Detection of breaking events in a wind-generated wave field. J. Phys. Oceanogr., 14, 16081619, doi:10.1175/1520-0485(1984)014<1608:DOBEIA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, J. M., 1981: Limiting gravity waves in water of finite depth. Philos. Trans. Roy. Soc. London, A302, 139188, doi:10.1098/rsta.1981.0159.

    • Search Google Scholar
    • Export Citation
  • Yuen, H. C., and B. M. Lake, 1980: Instabilities of waves on deep water. Annu. Rev. Fluid Mech., 12, 303334, doi:10.1146/annurev.fl.12.010180.001511.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 785 181 22
PDF Downloads 477 114 17