Abstract
In the conventional treatment of the coefficient of sea surface wind stress by plotting it against 10-m wind speed, there are inevitable discrepancies among results of various investigators. The reason is considered to lie primarily in the fact that the state of the sea surface or of waves is disregarded, which may have great influence on the sea surface wind stress.
Former concepts concerning the conditions which control the sea surface wind stress are discussed, and it is shown that a more universal expression may be obtained by plotting the coefficient against a kind of roughness Reynolds number:Re 2 *=u*H/ν, whereu* is the friction velocity of air, ν the kinematic viscosity of air, andH the characteristic wave height.H is used here to treat some data in wind-wave tunnels, as a tentative variable, one step towards a more rigorous approach to the problem.
This variableRe 2 *, orRe 4 *=u *w /L/v w =2πgu *w /v w n 1, where the subscript ω represents values for water,L andn 1 the characteristic wave length and frequency, respectively, is also the condition describing the air entrainment or the breaking of wind waves. In this case, these Reynolds numbers are interpreted as the quantity describing the intensity of turbulence of the water surface itself. It is shown, using data from our wind-wave tunnel experiments, that the breaking commences asRe 2 * reaches 1×103, or asRe 4 * reaches 3×103. Simultaneously, the stress-coefficient begins to increase sharply at this value ofRe 2 *. This phenomenon is understood as an increased momentum transfer from the air to the water through “boundary penetration of turbulence” caused by the breaking of wind waves. Further, it is suggested that there is a possibility that this excess momentum transfer does not increase wave momentum, but reinforces drift current.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Charnock, H. (1955): Wind stress on a water surface. Quart. Jour. Roy. Meteor. Soc.,81, 639–640.
Deacon, E. L. andE. K. Webb (1962): Interchange of properties between sea and air. Ch. 3. Small-scale interactions. In The Sea, edited byM. N. Hill, Interscience, New York, 43–87.
Francis, J. R. D. (1951): The aerodynamic drag of a free water surface. Proc. Roy. Soc. London, A,206, 387–406.
Hayami, S. andH. Kunishi (1959): A wind flume study on the generation of waves. Preprints, Proc. Intern. Oceanogr. Congr., Amer. Assoc. Adv. Sci., 753–755.
Kitaîgorodskiî, S. A. (1968): On the calculation of the aerodynamic roughness of the sea surface. Izv. Atmos. Ocean. Phys. Ser.,4, 870–878.
Kitaîgorodskiî, S. A., andYu. A. Volkov (1965): On the roughness parameter of the sea surface and the calculation of momentum flux in the near-water layer of the atmosphere. Izv. Atmos. Ocean. Phys. Ser.,1, 973–988.
Kraus, E. B. (1966): The aerodynamic roughness of the sea surface. Jour. Atmos. Sci.,23, 443–445.
Kraus, E. B. (1967): Wind stress along the sea surface. In Advances in Geophysics, vol.12, edited byH. E. Landsberg and J. vanMieghem, Academic Press, New York, 213–255.
Kraus, E. B. (1968): What do we know about the sea-surface wind stress. Bull. Amer. Meteor. Soc.,49, 247–253.
Kunishi, H. (1963): An experimental study on the generation and growth of wind waves. Disaster Prevention Res. Inst., Kyoto Univ., Bull., No. 61, 41 pp.
Kunishi, H. (1963a): An experimental study on the generation and growth of wind waves (second paper). Special Contributions of the Geoph. Inst., Kyoto Univ.,1, 93–98.
Kunishi, H. andN. Imasato (1966): On the growth of wind waves by high-speed wind flume. Disaster Prevention Res. Inst., Kyoto Univ., Annals9, 667–676 (in Japanese).
Lighthill, M. J. (1962): Physical interpretation of the mathematical theory of wave generation by wind. Jour. Fluid Mech.,14, 385–398.
Longuet-Higgins, M. S. (1969): On wave breaking and the equilibrium spectrum of wind-generated waves. Proc. Roy. Soc.A. 310, 151–159.
Miles, J. W. (1957): On the generation of surface waves by shear flows. Jour. Fluid Mech.,3, 185–204.
Monahan, E. C. (1966): A field study of sea spray and its relationship to low elevation wind speed-preliminary results. Woods Hole Oceanographic Institution, 147 pp.
Monin, A. S. andA. M. Yaglom (1965): Statistical Hydromechanics, Nauka, Moscow, 639 pp.
Munk, W. (1955): Wind stress on water: An hypothesis. Quart. Jour. Roy. Meteor. Soc.,81, 320–332.
Roll, H. U. (1948): Wassernahes Windprofil und Wellen auf dem Wattenmeer. Ann. Meteor.,1, 139–151.
Roll, H. U. (1965): Physics of the Marine Atmosphere. Academic Press, New York, 426 pp.
Stewart, R. W. (1961): The wave drag of wind over water. Jour. Fluid Mech.,10, 189–194.
Toba, Y. (1961): Drop production by bursting of air bubbles on the sea surface (III). Study by use of a wind flume. Memoirs, Coll. Sci., Univ. Kyoto, Ser. A,29, 313–344.
Van Dorn, W. G. (1953): Wind stress on an artificial pond. Jour. Marine Res.,12, 249–276.
Wu, J. (1968): Laboratory studies of wind-wave interactions. Jour. Fluid Mech.,34, 91–112.
Wu, J. (1969): Wind stress and surface roughness at air-sea interface. Jour. Geophys. Res.,74, 444–455.
Wu, J. (1969a): Froude number scaling of wind-stress coefficients. Jour. Atmos Sci.,26, 408–413.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Toba, Y., Kunishi, H. Breaking of wind waves and the sea surface wind stress. Journal of the Oceanographical Society of Japan 26, 71–80 (1970). https://doi.org/10.1007/BF02753814
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02753814