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On the generation of surface waves by shear flows. Part 5

Published online by Cambridge University Press:  28 March 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics,
Also Aerospace and Mechanical Engineering Sciences Department.
University of California, La Jolla
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Abstract

Laboratory and field measurements of the generation of gravity waves by turbulent winds imply that a theoretical model based on laminar flow may be adequate on a laboratory, but not an oceanographic, scale. This suggests that the significance of wave-induced perturbations in the turbulent Reynolds stresses for momentum transfer from wind to waves must increase with an appropriate scale parameter. A generalization of the laminar model is constructed by averaging the linearized equations of motion for a turbulent shear flow in a direction (say y) parallel to the wave crests of a particular Fourier component of the surface-wave field. It is shown that the resulting, mean momentum transfer to this component comprises: (i) a singular part, which is proportional to the product of the velocity-profile curvature and the mean square of the wave-induced vertical velocity in the critical layer, where the mean wind speed is equal to the wave speed; (ii) a vertical integral of the mean product of the vertical velocity and the vorticity ω, where ω is the wave-induced perturbation in the total vorticity along a streamline of the y-averaged motion; (iii) the perturbation in the mean turbulent shear stress at the air-water interface. The equation that governs the advection of the vorticity ω under the action of the perturbations in the turbulent Reynolds stresses is derived. Further theoretical progress appears to demand some ad hoc hypothesis for the specification of these turbulent Reynolds stresses. Two such hypotheses are discussed briefly, but it does not appear worth while, in the absence of more detailed experimental data, to carry out elaborate numerical calculations at this time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 1 , 17 October 1967 , pp. 163 - 175
Copyright
© 1967 Cambridge University Press

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References

Barnett, T. P. & Wilkerson, J. C. 1967 On the generation of wind waves as inferred from airborne radar measurements of fetch limited spectra. J. Mar. Res. (in the press).Google Scholar
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
Bryant, P. J. 1966 Wind generation of water waves. Ph.D. dissertation, University of Cambridge.
Cohen, L. S. & Hanratty, T. J. 1965 Generation of waves in the concurrent flow of air and a liquid. A.I.Ch.E.J. 11, 138–44.Google Scholar
Danner, W. P. 1966 A mixing length treatment of the effect of turbulence on the wind generation of water waves. M.Sc. dissertation, U.S. Naval Postgraduate School, Monterey.
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, vol. 1, p. 208. Oxford University Press.
Hamada, T. 1963 An experimental study of development of wind waves. Port and Harbour Res. Inst. (Japan) Rept. no. 2. Kanagawa.
Hanratty, T. J. & Woodmansee, P. E. 1965 Stability of the interface for a horizontal air-liquid flow. Proceedings of Symposium on Two-Phase Flow, vol. 1, p. A 101. Devon: University of Exeter.
Hasselmann, K. 1966 Interactions between ocean waves and the atmosphere. Sixth Symposium on Naval Hydrodynamics. Washington: Office of Naval Research (in the press).
Hidy, G. M. & Plate, E. J. 1966 Wind action on water standing in a laboratory channel. J. Fluid Mech. 26, 651–88.Google Scholar
Holmes, P. 1963 Wave generation by wind. Ph.D. dissertation, University of Wales (Swansea).
Landahl, M. T. 1967 A wave-guide model for turbulent shear flow. J. Fluid Mech. 29, 441.Google Scholar
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14, 385–98.Google Scholar
Longuet-Higgins M. S. 1962 The directional spectrum of ocean waves, and processes of wave generation. Proc. Roy. Soc. A 265, 286–315.Google Scholar
Longuet-Higgins, M. S., Cartwright, D. E. & Smith, P. E. 1963 Observations of the directional spectra of sea waves using the motions of a floating buoy. Ocean Wave Spectra, pp. 111–36. Edgewood Cliffs, N.J.: Prentice-Hall Inc.
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185–204.Google Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6, 568–82.Google Scholar
Miles, J. W. 1960 On the generation of surface waves by turbulent shear flows. J. Fluid Mech. 7, 469–78.Google Scholar
Miles, J. W. 1962 On the generation of surface waves by shear flows. Part 4. J. Fluid Mech. 13, 433–48.Google Scholar
Miles, J. W. 1965 A note on the interaction between surface waves and wind profiles. J. Fluid Mech. 22, 823–7.Google Scholar
Motzfield, H. 1937 Die turbulente Strömung un welligen Wanden. Z. angew. Math. Mech. 17, 193–212.Google Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–45.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Phillips, O. M. 1967 The maintenance of Reynolds stress in turbulent shear flow. J. Fluid Mech. 27, 131–44.Google Scholar
Pierson, W. J., Tick, L. J. & Baer, L. 1966 Computer based procedures for preparing global wave forecasts. Sixth Symposium on Naval Hydrodynamics. Washington: Office of Naval Research (in the Press).
Shemdin, O. H. & Hsu, E. Y. 1966 The dynamics of wind in the vicinity of progressive water waves. J. Fluid Mech. (in the press.)Google Scholar
Snyder, R. L. & Cox, C. S. 1966 A field study of the wind generation of ocean waves. J. Mar. Res. 24, 141–78.Google Scholar
Stewart, R. W. 1961 The wave drag of wind over water. J. Fluid Mech. 10, 189–94.Google Scholar
Sverdrup, H. U. & Munk, W. 1947 Wind, sea and swell. Publ. Hydrog. Off., Wash., no. 601.
Taylor, G. I. 1915 Eddy motion in the atmosphere. Phil. Trans. A 215, 1–26; Scientific Papers 2, 1–24.Google Scholar
Wiegel, R. L. & Cross, R. H. 1966 Generation of wind waves. J. Waterways and Härbors Div., ASCE 92, 1–26.Google Scholar
Zagustin, K., Hsu, E. Y., Street, R. L. & Perry, B. 1966 Flow over a moving boundary in relation to wind-generated waves. Dept. Civil Engng Tech. Rep. no. 60, Stanford University.Google Scholar