Skip to main content

A Parameter Describing Overall Conditions of Wave Breaking, Whitecapping, Sea-Spray Production and Wind Stress

  • Chapter
Oceanic Whitecaps

Part of the book series: Oceanographic Sciences Library ((OCSL,volume 2))

Abstract

The dim ensionless parameter u 2* /vσ can be used widely as a parameter to describe the overall conditions of air-sea boundary processes, where u* is the friction velocity of air, v is the kinematic viscosity of air and s is the spectral peak frequency of the wind waves. A critical value of this parameter for the appreciable commencement of breaking of wind waves is 103. Beyond this value, the percentage of waves passing a fixed point that are breaking, α, and the percentage of whitecap coverage, P, are both approximately proportional to this parameter. The number concentration of sea-salt particles containing salt in the vicinity of 10−10 g at the 6-m level is also proportional to this parameter. The dimensionless roughness length associated with the air flow over water, u*Z0 /V, also correlates better with this parameter than with a parameter which does not contain the spectral peak frequency. This gives an approximate relation of z0 σ/u* = 0.025, and a corresponding formula for the drag coefficient is proposed. The dimensional and physical interpretation of the parameteru */2/vσ is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Banner, M. L. & O. M. Phillips (1974): On the incipient breaking of small-scale waves. J. Fluid Mech., 65, 647–656.

    Article  Google Scholar 

  • Blanchard, D. C. & A. H. Woodcock (1980): The production, concentration and vertical distribution of the sea-salt aerosol. Annals, New York Acad. Sci., 338, 330–347.

    Article  Google Scholar 

  • Chaen, M. (1973): Studies on the production of sea-salt particles on the sea surface. Mem. Fac. Fish., Kago-shima Univ., 22, 49–107.

    Google Scholar 

  • Charnock, H. (1955): Wind stress on a water surface. Quart. J.Roy. Meteor. Soc., 81, 639–640.

    Article  Google Scholar 

  • Garratt, J. R. (1977): Review of dragcoefficients over oceans and continents. Mon. Wea. Rev., 105, 915–929.

    Article  Google Scholar 

  • Hamada, T. (1963): An experimental study of development of wind waves. Rep. Port and Harbour Tech. Res. Inst., No. 2, 1–41.

    Google Scholar 

  • Hatori, M. & Y. Toba (1983): Transition of mechanically generated regular waves to wind waves under the action of wind. J. Fluid Mech., 130, 397–409.

    Article  Google Scholar 

  • Kawai, S. (1979): Generation of initial wavelets by instability of a coupled shear flow and their evolution to wind waves. J. Fluid Mech., 93, 661–703.

    Article  Google Scholar 

  • Kawai, S. (1982): Structure of the air flow over wind wave crests revealed by flow visualization techniques. Boundary-Layer Met., 23, 503–521.

    Article  Google Scholar 

  • Kawai, S., K. Okada & Y. Toba (1977): Field data support of three-seconds power law and gu* σ−4-spectral form for growing wind waves. J. Oceanogr. Soc. Japan, 33, 137–150.

    Article  Google Scholar 

  • Kawamura, H., K. Okuda, S. Kawai & Y. Toba (1981): Structure of turbulent boundary layer over wind waves in a wind wave tunnel. Tokohu Geophys. Journ. (Sci. Rep. Tohoku Univ. Ser. 5), 28, 69–86.

    Google Scholar 

  • Kitaigorodsky, S. A. (1968): On the calculation of aerodynamic roughness of the sea surface. Izv. Akad. Sci. USSR, Atmos. Ocean.Phys., 4, 870–878.

    Google Scholar 

  • Kitaigorodskii, S. A. (1969): Small-scale atmosphere-ocean interactions. Izv. Akad. Sci. USSR, Atmos. Ocean.Phys., 5, 1114–1131

    Google Scholar 

  • Kitaigorodskii, S. A. & M. M. Zaslavsky (1974): A dynamical analysis of the drag conditions at the sea surface. Boundary-Layer Met., 6, 53–61.

    Google Scholar 

  • Koga, M. (1981): Detailed structure of breaking wind waves with droplet and bubble formation. Ph.D. dissertation at Division of Science, Tohoku University, 163 pp.

    Google Scholar 

  • Koga, M. (1981a): Direct production of droplets from breaking wind waves — its observation by a multicolored overlapping exposure photographing technique. Tellus, 33, 552–563.

    Article  Google Scholar 

  • Koga, M. & Y. Toba (1981): Droplet distribution and dispersion process on breaking wind waves. Tohoku Geophys. Journ. (Sci. Rep. Tokohu Univ. Ser. 5), 28, 1–25.

    Google Scholar 

  • Kondo, J., Y. Fujinawa & G. Naito (1973): High-frequency components of ocean waves and their relation to the aerodynamic roughness.J. Phys. Oceanogr., 3, 197–202.

    Article  Google Scholar 

  • Kunishi, H. (1963): An experimental study on the generation and growth of wind waves. Bull. Disas. Prev. Res. Inst. Kyoto Univ., No. 61, 1–41.

    Google Scholar 

  • Kunishi, H. & N. Imasato (1966): On the growth of wind waves by high-speed wind flume. Disas. Prev. res. Inst. Kyoto Univ., Annals, 9, 1–10 (in Japanese with English abstract).

    Google Scholar 

  • Longuet-Higgins, M. S. (1978a): The instabilities of gravity waves of finite amplitude in deep water. I. Superharmonics.Proc.R.Soc.Lond. A360, 471–488.

    Google Scholar 

  • Longuet-Higgins, M. S. (1978b): The instabilities of gravity waves of finite amplitude in deep water. II. Subharmonics. Proc. Roy. Soc. Lond. A360, 489–505.

    Google Scholar 

  • McLean, J. W. (1982): Instabilities of finite-amplitude water waves. J. Fluid Mech., 114, 315–330.

    Article  Google Scholar 

  • Melville, W. K. (1977): Wind stress and surface roughness over breaking waves. J. Phys. Oceanogr., 7, 702–710.

    Article  Google Scholar 

  • Melville, W. K. (1982): The instability of deep-water waves. J. Fluid Mech., 115, 165–185.

    Article  Google Scholar 

  • Mitsuyasu, H., R. Nakayama & T. Komori (1971): Observations of the winds and waves in Hakata Bay. Rep. Res. Inst. Appl. Mech., Kyushu Univ., 19, 37–74.

    Google Scholar 

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

    Article  Google Scholar 

  • Monahan, E. C., C. W. Fairall, K. L. Davidson & P. J. Boyle (1983): Observed inter-relations between 10m winds, ocean whitecaps and marine aerosols. Quart. J. R. Met. Soc., 109, 379–392.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Munk, W. H. (1955): Wind stress on water, ahypothesis. Quart. J. Roy.Met. Soc., 81, 320–322.

    Article  Google Scholar 

  • Nordberg, W., J. Conway, D. B. Ross & T. Wilheit (1971): Measurements of microwave emission from a foam-covered, wind-driven sea. J. Atmos. Sci., 28, 429–435.

    Article  Google Scholar 

  • Okuda, K. (1982): Internal flow structure of short wind waves. Part 1. On the internal vorticity structure. J. Oceanogr. Soc. Japan, 38, 28–42.

    Article  Google Scholar 

  • Okuda, K., S. Kawai & Y. Toba (1977): Measurement of skin friction distribution along the surface of wind waves. J. Oceanogr. Soc.Japan, 33, 190–198.

    Article  Google Scholar 

  • Phillips, O. M. & M.L. Banner (1974): Wave breaking in the presence of wind drift and swell. J. Fluid Mech., 66, 625–640.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Su, M.-Y., M. Bergin, P. Marler & R. Myrick (1982): Experiments on nonlinear instabilities and evolution of steep gravity-wave trains.J. Fluid Mech., 124, 45–72.

    Article  Google Scholar 

  • The SWAMP group (1983): Seawavemodellingproject (SWAMP) Part 1. Proc, IUCRM Symp. on Wave Dynamics and Radio Probing of the Ocean Surface, May 13–20, 1981, Miami Beach (inpress).

    Google Scholar 

  • Toba, Y. (1961): Drop production by bursting of air bubbles on the seasurface.III. Study by use of a wind flume. Mem. College Sci., Univ. of Kyoto, Ser. A, 29, 313–344.

    Google Scholar 

  • Toba, Y. (1972): Local balance in the air-sea boundary processes. I. On the growth processof wind waves.J.Oceanogr. Soc. Japan, 28, 109–120.

    Article  Google Scholar 

  • Toba, Y. (1978): Stochastic form of the growth of wind waves in a single-parameter representation with physical implications. J. Phys. Oceanogr., 8, 494–507.

    Article  Google Scholar 

  • Toba, Y. (1979): Study on wind waves as a strongly nonlinear phenomenon. Twelfth Symp. on Naval Hydrodyn., Nat. Acad. of Sci., Wash., D.C., 529–540.

    Google Scholar 

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

    Google Scholar 

  • Toba, Y., H. Kawamura & K. Okuda (1984): Ordered motions in turbulent boundary layers above and below wind waves. Turbulence and Chaotic Phenomena in Fluids, ed. by T. Tatsumi, North Holland Pub. Co., 513–518.

    Google Scholar 

  • Toba, Y. & H. Kunishi (1970): Breaking of wind waves and the sea surface wind stress.J. Oceanogr. Soc. Japan, 26, 71–80.

    Article  Google Scholar 

  • Toba, Y., H. Kunishi, K. Nishi, S. Kawai, Y. Shimada & N. Shibata (1971): Study on the air-sea boundary processes at the Shirahama Oceanographic Tower Station. Disas. Prev. Res. Inst. Kyoto Univ, Annals, 14B, 519–531 (in Japanese with English abstract).

    Google Scholar 

  • Toba, Y., M. Tokuda, K. Okuda & S. Kawai (1975): Forced convection accompanying wind waves. J. Oceanogr. Soc. Japan, 31, 192–198.

    Article  Google Scholar 

  • Tokuda, M. & Y. Toba (1981): Statistical characteristics of individual waves in laboratory wind waves. I. Individual wave spectra and similarity structure.J. Oceanogr. Soc.Japan, 37, 243–258.

    Article  Google Scholar 

  • Woodcock, A. H. (1953): Salt nuclei in marine air as a function of altitude and wind force. J. Meteor., 10, 362–371.

    Article  Google Scholar 

  • Wu, J. (1979): Oceanic whitecapsandseastate. J. Phys. Oceanogr., 9, 1064–1068.

    Article  Google Scholar 

  • Wu, J. (1980): Wind-stress coefficients over sea surface near neutral conditions-A revisit. J. Phys. Oceanogr., 10, 727–740.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 D. Reidel Publishing Company

About this chapter

Cite this chapter

Toba, Y., Koga, M. (1986). A Parameter Describing Overall Conditions of Wave Breaking, Whitecapping, Sea-Spray Production and Wind Stress. In: Monahan, E.C., Niocaill, G.M. (eds) Oceanic Whitecaps. Oceanographic Sciences Library, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4668-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4668-2_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8575-5

  • Online ISBN: 978-94-009-4668-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics