• Andreas, E. L., 2004: Spray stress revisited. J. Phys. Oceanogr., 34 , 14291440.

  • Banner, M. L., 1990: The influence of wave breaking on the surface pressure distribution in wind-wave interactions. J. Fluid Mech., 211 , 463495.

    • Search Google Scholar
    • Export Citation
  • Banner, M. L., , and D. H. Peregrine, 1993: Wave breaking in deep water. Annu. Rev. Fluid Mech., 25 , 373397.

  • Belcher, S. E., , and J. C. Vassilicos, 1997: Breaking waves and the equilibrium range of wind-wave spectra. J. Fluid Mech., 342 , 377401.

    • Search Google Scholar
    • Export Citation
  • Caulliez, G., 2002: Self-similarity of near-breaking short gravity wind waves. Phys. Fluids, 14 , 29172920.

  • Coceal, O., , and S. E. Belcher, 2004: A canopy model of mean winds through urban areas. Quart. J. Roy. Meteor. Soc., 130 , 13491372.

  • Cohen, I. M., , and P. K. Kundu, 2002: Fluid Dynamics. 2d ed. Academic Press, 730 pp.

  • Donelan, M. A., , B. K. Haus, , N. Reul, , W. J. Plant, , M. Stiassnie, , H. C. Graber, , O. B. Brown, , and E. S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett., 31 .L18306, doi:10.1029/2004GL019460.

    • Search Google Scholar
    • Export Citation
  • Drennan, W. M., , H. C. Graber, , D. Hauser, , and C. Quentin, 2003: On the wave age dependence of wind stress over pure wind seas. J. Geophys. Res., 108 .8062, doi:10.1029/2000JC000715.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J., 2005: On the occurrence of wave breaking. Rogue Waves: Proc. 14th ’Aha Huliko’a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 123–130.

  • Hara, T., , and S. E. Belcher, 2002: Wind forcing in the equilibrium range of wind-wave spectra. J. Fluid Mech., 470 , 223245.

  • Hara, T., , and S. E. Belcher, 2004: Wind profile and drag coefficient over mature ocean surface wave spectra. J. Phys. Oceanogr., 34 , 23452358.

    • Search Google Scholar
    • Export Citation
  • Jones, I. S. F., , and Y. Toba, Eds. 2001: Wind Stress over the Ocean. Cambridge University Press, 307 pp.

  • Komen, G. J., , L. Cavaleri, , M. Donelan, , K. Hasselmann, , S. Hasselmann, , and P. A. E. M. Janssen, Eds. 1996: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532 pp.

  • Kudryavtsev, V. N., , and V. K. Makin, 2001: The impact of air-flow separation on the drag of the sea surface. Bound.-Layer Meteor., 98 , 155171.

    • Search Google Scholar
    • Export Citation
  • Kukulka, T., , and T. Hara, 2005: Momentum flux budget analysis of wind-driven air-water interfaces. J. Geophys. Res., 110 .C12020, doi:10.1029/2004JC002844.

    • Search Google Scholar
    • Export Citation
  • Makin, V. K., , and C. Mastenbroek, 1996: Impact of waves on air-sea exchange of sensible heat and momentum. Bound.-Layer Meteor., 79 , 279300.

    • Search Google Scholar
    • Export Citation
  • Makin, V. K., , and V. N. Kudryavtsev, 1999: Coupled sea surface-atmosphere model. 1. Wind over waves coupling. J. Geophys. Res., 104 , C4. 76137624.

    • 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.

  • Melville, W. K., , and P. Matusov, 2002: Distribution of breaking waves at the ocean surface. Nature, 417 , 5863.

  • Phillips, O., 1985: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech., 156 , 505531.

    • Search Google Scholar
    • Export Citation
  • Phillips, O., , F. L. Posner, , and J. P. Hansen, 2001: High range resolution radar measurements of the speed distribution of breaking events in wind-generated ocean waves: Surface impulse and wave energy dissipation rates. J. Phys. Oceanogr., 31 , 450460.

    • Search Google Scholar
    • Export Citation
  • Reul, N., , H. Branger, , and J-P. Giovanangeli, 1999: Air flow separation over unsteady breaking waves. Phys. Fluids, 11 , 19591961.

  • Thorpe, S., 1993: Energy loss by breaking waves. J. Phys. Oceanogr., 23 , 24982502.

  • Thorpe, S., 2005: The Turbulent Ocean. Cambridge University Press, 439 pp.

  • Toba, Y., , and N. Ebuchi, 1991: Sea-surface roughness length fluctuating in concert with wind and waves. J. Oceanogr. Soc. Japan, 47 , 6379.

    • Search Google Scholar
    • Export Citation
  • Toba, Y., , N. Iida, , H. Kawamura, , N. Ebuchi, , and I. S. Jones, 1990: Wave dependence of sea-surface wind stress. J. Phys. Oceanogr., 20 , 705721.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 74 73 14
PDF Downloads 45 45 9

A Model of the Air–Sea Momentum Flux and Breaking-Wave Distribution for Strongly Forced Wind Waves

View More View Less
  • 1 Graduate School of Oceanography, University of Rhode Island, Narragansett, Rhode Island
  • | 2 Department of Meteorology, University of Reading, Reading, United Kingdom
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

Under high-wind conditions, breaking surface waves likely play an important role in the air–sea momentum flux. A coupled wind–wave model is developed based on the assumption that in the equilibrium range of surface wave spectra the wind stress is dominated by the form drag of breaking waves. By conserving both momentum and energy in the air and also imposing the wave energy balance, coupled equations are derived governing the turbulent stress, wind speed, and the breaking-wave distribution (total breaking crest length per unit surface area as a function of wavenumber). It is assumed that smaller-scale breaking waves are sheltered from wind forcing if they are in airflow separation regions of longer breaking waves (spatial sheltering effect). Without this spatial sheltering, exact analytic solutions are obtained; with spatial sheltering asymptotic solutions for small- and large-scale breakers are derived. In both cases, the breaking-wave distribution approaches a constant value for large wavenumbers (small-scale breakers). For low wavenumbers, the breaking-wave distribution strongly depends on wind forcing. If the equilibrium range model is extended to the spectral peak, the model yields the normalized roughness length (Charnock coefficient) of growing seas, which increases with wave age and is roughly consistent with earlier laboratory observations. However, the model does not yield physical solutions beyond a critical wave age, implying that the wind input to the wave field cannot be dominated by breaking waves at all wavenumbers for developed seas (including field conditions).

Corresponding author address: Tobias Kukulka, Graduate School of Oceanography, University of Rhode Island, Narragansett, RI 02882. Email: tkukulka@gso.uri.edu

Abstract

Under high-wind conditions, breaking surface waves likely play an important role in the air–sea momentum flux. A coupled wind–wave model is developed based on the assumption that in the equilibrium range of surface wave spectra the wind stress is dominated by the form drag of breaking waves. By conserving both momentum and energy in the air and also imposing the wave energy balance, coupled equations are derived governing the turbulent stress, wind speed, and the breaking-wave distribution (total breaking crest length per unit surface area as a function of wavenumber). It is assumed that smaller-scale breaking waves are sheltered from wind forcing if they are in airflow separation regions of longer breaking waves (spatial sheltering effect). Without this spatial sheltering, exact analytic solutions are obtained; with spatial sheltering asymptotic solutions for small- and large-scale breakers are derived. In both cases, the breaking-wave distribution approaches a constant value for large wavenumbers (small-scale breakers). For low wavenumbers, the breaking-wave distribution strongly depends on wind forcing. If the equilibrium range model is extended to the spectral peak, the model yields the normalized roughness length (Charnock coefficient) of growing seas, which increases with wave age and is roughly consistent with earlier laboratory observations. However, the model does not yield physical solutions beyond a critical wave age, implying that the wind input to the wave field cannot be dominated by breaking waves at all wavenumbers for developed seas (including field conditions).

Corresponding author address: Tobias Kukulka, Graduate School of Oceanography, University of Rhode Island, Narragansett, RI 02882. Email: tkukulka@gso.uri.edu

Save