Cover Journal of Physical Oceanography
Journal of Physical Oceanography

  • Andreas, E. L., 1992: Sea spray and the turbulent air-sea heat fluxes. J. Geophys. Res., 97 , 11 429–11 441.

  • Anguelova, M. D., and F. Webster, 2006: Whitecap coverage from satellite measurements: A first step toward modeling the variability of oceanic whitecaps. J. Geophys. Res., 111 , C03017. doi:10.1029/2005JC003158.

    • Search Google Scholar
    • Export Citation

  • Asher, W., and R. Wanninkhof, 1998: The effects of bubble-mediated gas transfer on purposeful dual-gaseous tracer experiment. J. Geophys. Res., 103 , 10 555–10 560.

    • Search Google Scholar
    • Export Citation

  • Babanin, A. V., I. R. Young, and M. L. Banner, 2001: Breaking probabilities for dominant surface waves on water of finite constant depth. J. Geophys. Res., 106 , 11 659–11 676.

    • Search Google Scholar
    • Export Citation

  • Banner, M. L., and O. M. Phillips, 1974: On the incipient breaking of small scale breaking waves. J. Fluid Mech., 65 , 647–657.

  • Banner, M. L., and D. H. Peregrine, 1993: Wave breaking in deep water. Annu. Rev. Fluid Mech., 25 , 373–395.

  • Banner, M. L., and I. R. Young, 1994: Modeling spectral dissipation in the evolution of wind waves. Part I: Assessment of existing model performance. J. Phys. Oceanogr., 24 , 1550–1571.

    • Search Google Scholar
    • Export Citation

  • Banner, M. L., and X. Tian, 1998: On the determination of the onset of breaking for modulating surface gravity water waves. J. Fluid Mech., 367 , 107–137.

    • Search Google Scholar
    • Export Citation

  • Banner, M. L., A. V. Babanin, and I. R. Young, 2000: Breaking probability for dominant waves on the sea surface. J. Phys. Oceanogr., 30 , 3145–3160.

    • Search Google Scholar
    • Export Citation

  • Benjamin, T., and J. Feir, 1967: The disintegration of wave trains in deep water. J. Fluid Mech., 27 , 373–397.

  • Bortkovskii, R., 1987: Air–Sea Exchange of Heat and Moisture during Storms. D. Reidel, 193 pp.

  • Buckingham, E., 1914: On physically similar systems: Illustrations of the use of dimensional analysis. Phys. Rev., 4 , 345.

  • Cartwright, D. E., and M. S. Longuet-Higgins, 1956: The statistical distribution of the maxima of a random function. Proc. Roy. Soc. London, 237 , 212–232.

    • Search Google Scholar
    • Export Citation

  • Clift, R., J. R. Grace, and M. E. Weber, 1978: Bubbles, Drops, and Particles. Academic Press, 380 pp.

  • Deane, G. B., and M. D. Stokes, 2002: Scale dependence of bubble creation mechanisms in breaking waves. Nature, 418 , 839–844.

  • Donelan, M. A., 1990: Air–sea interaction. The Sea, B. L. Mehaute and D. M. Hanes, Eds., Vol. 9, Ocean Engineering Science, Wiley-Interscience, 239–292.

    • Search Google Scholar
    • Export Citation

  • Doyle, D., 1984: Whitecaps and marine atmosphere rep. 6. University College, Galway, Ireland, 140 pp.

  • Duncan, J. H., 1981: An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. Roy. Soc. London, 377A , 331–348.

    • Search Google Scholar
    • Export Citation

  • Duncan, J. H., 1983: The breaking and non-breaking wave resistance of a two-dimensional hydrofoil. J. Fluid Mech., 126 , 507–520.

  • Garrett, C., M. Li, and D. Farmer, 2000: The connection between bubble size spectra and energy dissipation rates in the upper ocean. J. Phys. Oceanogr., 30 , 2163–2171.

    • Search Google Scholar
    • Export Citation

  • Gordon, H. R., 1997: Atmospheric correction of ocean color imagery in the Earth Observing System era. J. Geophys. Res., 102 , 17 081–17 106.

    • Search Google Scholar
    • Export Citation

  • Hanson, J., and O. Phillips, 1999: Wind sea growth and dissipation in the open ocean. J. Phys. Oceanogr., 29 , 1633–1648.

  • Jones, I. S. F., and Y. Toba, 2001: Wind Stress over the Ocean. Cambridge University Press, 307 pp.

  • Kalvoda, P. M., L. L. Xu, and J. Wu, 2003: Macrobubble clouds produced by breaking wind waves: A laboratory study. J. Geophys. Res., 108 , 3207. doi:10.1029/1999JC000265.

    • Search Google Scholar
    • Export Citation

  • Kinsman, B., 1965: Wind Waves. Prentice-Hall, 676 pp.

  • Kjeldsen, S. P., and D. Myrhaug, 1980: Wave-wave interactions, current-wave interactions and resulting extreme waves and breaking waves. Proc. 17th Conf. on Coastal Engineering, Sydney, Australia, American Society of Civil Engineers, 2277–2303.

    • Search Google Scholar
    • Export Citation

  • Komen, G. J., L. Cavaleri, M. A. Donelan, K. Hasselmann, S. Hasselmann, and P. A. E. M. Janssen, 1994: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532 pp.

    • Search Google Scholar
    • Export Citation

  • Kway, J. H. L., Y. S. Loh, and E. S. Chan, 1998: Laboratory study of deep-water breaking waves. Ocean Eng., 25 , 657–676.

  • Lafon, C., J. Piazzola, P. Forget, O. Le Calvé, and S. Despiau, 2004: Analysis of the variations of the whitecap fraction as measured in a coastal zone. Bound.-Layer Meteor., 111 , 339–360.

    • Search Google Scholar
    • Export Citation

  • Lafon, C., J. Piazzola, P. Forget, and S. Despiau, 2007: Whitecap coverage in coastal environment for steady and unsteady wave field conditions. J. Mar. Syst., 66 , 38–46.

    • Search Google Scholar
    • Export Citation

  • Lamarre, E., and W. K. Melville, 1991: Air entrainment and dissipation in breaking waves. Nature, 351 , 469–472.

  • Lamb, H., 1953: Hydrodynamics. Cambridge University Press, 420 pp.

  • Leifer, I., R. K. Patro, and P. Bowyer, 2000: A study on the temperature variation of rise velocity for large clean bubbles. J. Atmos. Oceanic Technol., 17 , 1392–1402.

    • Search Google Scholar
    • Export Citation

  • Longuet-Higgins, M. S., 1952: On the statistical distribution of the heights of the sea waves. J. Mar. Res., 11 , 245–266.

  • Longuet-Higgins, M. S., 1957: The statistical analysis of a random, moving surface. Philos. Trans. Roy. Soc. London, 249A , 321–387.

    • Search Google Scholar
    • Export Citation

  • Longuet-Higgins, M. S., 1958: On the interval between successive zeros of a random function. Proc. Roy. Soc. London, 246A , 99–118.

    • Search Google Scholar
    • Export Citation

  • Longuet-Higgins, M. S., 1969: On wave breaking and equilibrium spectrum of wind. Proc. Roy. Soc. London, 310A , 151–159.

  • Longuet-Higgins, M. S., and R. W. Stuart, 1961: The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech., 10 , 529–549.

    • Search Google Scholar
    • Export Citation

  • Martsinkevich, L. M., and V. V. Melent’ev, 1975: The relation of the radio brightness temperature of a wavy sea to the sea state characteristics and the wave generating factors. USSR/USA Bering Sea Experiment, K. Ya. Kondrat’Ev, W. Nordberg, and Yu. I. Rabinovich, Eds., Oxonian Press, 126–148.

    • Search Google Scholar
    • Export Citation

  • Melville, W. K., 1996: The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech., 28 , 279–321.

  • Monahan, E. C., 1971: Oceanic whitecaps. J. Phys. Oceanogr., 1 , 139–144.

  • Monahan, E. C., 1993: Occurrence and evolution of acoustically relevant sub-surface bubble plumes and their associated, remotely monitorable surface whitecaps. Natural Physical Sources of Underwater Sound, B. V. R. Kerman, Ed., Kluwer Academic, 503–517.

    • Search Google Scholar
    • Export Citation

  • Monahan, E. C., and I. O’Muircheartaigh, 1980: Optimal power-law description of oceanic whitecap coverage dependence on wind speed. J. Phys. Oceanogr., 10 , 2094–2099.

    • Search Google Scholar
    • Export Citation

  • Monahan, E. C., and I. O’Muircheartaigh, 1986: Whitecaps and the passive remote sensing of the ocean surface. Int. J. Remote Sens., 7 , 627–642.

    • Search Google Scholar
    • Export Citation

  • Monahan, E. C., and M. Lu, 1990: Optimal power-law description of oceanic whitecap coverage dependence on wind speed. J. Phys. Oceanogr., 10 , 2094–2099.

    • Search Google Scholar
    • Export Citation

  • Monahan, E. C., P. Bowyer, D. Doyle, M. Higgins, and D. Woolf, 1985: Whitecaps and marine atmosphere rep. 8. University College, Galway, Ireland, 124 pp.

    • Search Google Scholar
    • Export Citation

  • Moore, K. D., K. J. Voss, and H. R. Gordon, 2000: Spectral reflectance of whitecaps: Their contribution to water-leaving radiance. J. Geophys. Res., 105 , 6493–6499.

    • Search Google Scholar
    • Export Citation

  • Phillips, O. M., 1977: The Dynamics of the Upper Ocean. Cambridge University Press, 207 pp.

  • Rapp, R. J., and W. K. Melville, 1990: Laboratory measurements of deep water breaking waves. Philos. Trans. Roy. Soc. London, 331A , 735–780.

    • Search Google Scholar
    • Export Citation

  • Rice, S. O., 1944: Mathematical analysis of random noise. Bell Syst. Tech. J., 23 , 282–332.

  • Ross, D., and V. Cardone, 1974: Observations of oceanic whitecaps and their relation to remote measurements of surface wind speed. J. Geophys. Res., 79 , 444–452.

    • Search Google Scholar
    • Export Citation

  • Snyder, R., L. Smith, and R. Kennedy, 1983: On the formation of whitecaps by a threshold mechanism. Part III: Field experiment and comparison with theory. J. Phys. Oceanogr., 13 , 1505–1518.

    • Search Google Scholar
    • Export Citation

  • Stramska, M., and T. Petelski, 2003: Observations of oceanic whitecaps in the north polar waters of the Atlantic. J. Geophys. Res., 108 , 3086. doi:10.1029/2002JC001321.

    • Search Google Scholar
    • Export Citation

  • Stramski, D., and J. Tegowski, 2001: Effects of intermittent entrainment of air bubbles by breaking wind waves on ocean reflectance and underwater light field. J. Geophys. Res., 106 , 31 345–31 360.

    • Search Google Scholar
    • Export Citation

  • Sugihara, Y., H. Tsumori, T. Ohga, H. Yoshioka, and S. Serizawa, 2007: Variation of whitecap coverage with wave-field conditions. J. Mar. Syst., 66 , 47–60.

    • Search Google Scholar
    • Export Citation

  • Thorpe, S. A., 1982: On the clouds of bubbles formed by breaking wind-waves in deep water, and their role in air-sea gas transfer. Philos. Trans. Roy. Soc. London, 304A , 155–210.

    • Search Google Scholar
    • Export Citation

  • Toba, Y., 1972: Local balance in the air-sea boundary processes. J. Oceanogr. Soc. Japan, 28 , 109–120.

  • Toba, Y., and M. Chaen, 1973: Quantitative expression of the breaking of wind waves on the sea surface. Rec. Oceanogr. Works Japan, 12 , 1–11.

    • Search Google Scholar
    • Export Citation

  • Wu, C. H., and H. M. Nepf, 2002: Breaking criteria and energy losses for three-dimensional wave breaking. J. Geophys. Res., 107 , 3177. doi:10.1029/2001JC001077.

    • Search Google Scholar
    • Export Citation

  • Wu, J., 1975: Wind-induced drift currents. J. Fluid Mech., 69 , 49–70.

  • Wu, J., 1988: Oceanic whitecaps and sea state. J. Phys. Oceanogr., 9 , 1064–1068.

  • Young, I. R., and A. V. Babanin, 2006: Spectral distribution of energy dissipation of wind-generated waves due to dominant wave breaking. J. Phys. Oceanogr., 36 , 376–394.

    • Search Google Scholar
    • Export Citation

  • Yuan, Y. L., F. Hua, and Z. D. Pan, 1988: Wave breaking statistics and its application in upper ocean dynamics. Sci. China, Ser. B, 10 , 1084–1091.

    • Search Google Scholar
    • Export Citation

  • Yuan, Y. L., F. Hua, S. W. Zhang, and L. Han, 2008: Statistical model on the surface elevation of waves with breaking. Sci. China, Ser. D, 51 , 759–768.

    • Search Google Scholar
    • Export Citation

  • Zhao, D., and Y. Toba, 2001: Dependence of whitecap coverage on wind and wind-wave properties. J. Oceanogr., 57 , 603–616.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 73 38 2
PDF Downloads 36 16 1
Editorial Type:
Article
Article Type:
Research Article

The Statistical Theory of Breaking Entrainment Depth and Surface Whitecap Coverage of Real Sea Waves

Yeli Yuan1, Lei Han1, Feng Hua1, Shuwen Zhang2, Fangli Qiao3, Yongzeng Yang3, and Changshui Xia3
View More View Less
  • 1 First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong, China
  • | 2 South China Sea Environmental Institute, Guangdong Ocean University, Zhanjiang, Guangdong, China
  • | 3 First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong, China
Print Publication:
01 Jan 2009
DOI:
https://doi.org/10.1175/2008JPO3944.1
Page(s):
143–161
Restricted access

Abstract

Some basic statistics for wave breaking have been derived based on the statistical model of real sea waves. The analytic expressions of breaking entrainment depth and surface whitecap coverage involved with both sea wave characteristics and surface wind velocity have been derived on the basis of the whitecap formation model. The concept of the upper envelope for all the whitecap coverage data versus wind speed has been proposed, and it is assumed to correspond to the whitecap coverage in the case of the infinite wind duration and fetch to determine the model constants. The analytic expressions of breaking entrainment depth and whitecap coverage have been compared with the observations in several ways, and consistently favorable agreement can be found for most observations.

Corresponding author address: Dr. Lei Han, First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong, China. Email: hanlei@fio.org.cn

Abstract

Some basic statistics for wave breaking have been derived based on the statistical model of real sea waves. The analytic expressions of breaking entrainment depth and surface whitecap coverage involved with both sea wave characteristics and surface wind velocity have been derived on the basis of the whitecap formation model. The concept of the upper envelope for all the whitecap coverage data versus wind speed has been proposed, and it is assumed to correspond to the whitecap coverage in the case of the infinite wind duration and fetch to determine the model constants. The analytic expressions of breaking entrainment depth and whitecap coverage have been compared with the observations in several ways, and consistently favorable agreement can be found for most observations.

Corresponding author address: Dr. Lei Han, First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong, China. Email: hanlei@fio.org.cn

Save