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Oblique wind waves generated by the instability of wind blowing over water

Published online by Cambridge University Press:  26 April 2006

L. C. Morland
Affiliation:
Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA

Abstract

The growth rates of gravity waves are computed from linear, inviscid stability theory for wind velocity profiles that are representative of the mean flow in a turbulent boundary layer. The energy transfer to the waves is largely concentrated in an angle (to the wind) interval that broadens with increasing wind speed and narrows with increasing wavelength. At sufficiently high wind speeds and sufficiently short wavelengths, the waves of maximum growth rate propagate at an oblique angle to the wind. The connection with bimodal directional distributions of observed spectra is discussed.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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References

Banner, M. L. & Melville, W. K. 1976 On the separation of air flow over water waves. J. Fluid Mech. 77, 825842.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1993 Turbulent shear flow over slowly moving waves. J. Fluid Mech. 251, 109148.Google Scholar
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161205.Google Scholar
Burgers, G. & Makin, V. K. 1993 Boundary-layer model results for wind-sea growth. J. Phys. Oceanogr. 23, 372385.Google Scholar
Coté, L. J., Davis, J. O., Marks, W. et al. 1960 The directional spectrum of a wind generated sea as determined from data obtained by the Stereo Wave Observation Project. New York University College of Engineering, Meteorol. Paper, 2, No. 6, 88 pp.
Donelan, M. A., Hamilton, J. & Hui, W. H. 1985 Directional spectra of wind-generated waves. Phil. Trans. R. Soc. Lond. A 315, 509562.Google Scholar
Duin, C. A. VAN & Janssen, P. A. E. M. 1992 An analytical model of the generation of surface gravity waves by turbulent air flow. J. Fluid Mech. 236, 197215.Google Scholar
Jackson, F. C., Walton, W. T. & Peng, C. Y. 1985 A comparison of in situ and airborne radar observations of ocean wave directionality. J. Geophys. Res. 90 (C1), 10051018.Google Scholar
Jacobs, S. J. 1987 An asymptotic theory for the turbulent flow over a progressive water wave. J. Fluid Mech. 174, 6980.Google Scholar
Knight, D. 1977 Turbulent flow over a wavy boundary. Boundary-Layer Met. 11, 205222.Google Scholar
Lamb, H. 1945 Hydrodynamics, 6th edn. Dover.
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185204.Google Scholar
Miles, J. W. 1962 On the generation of surface waves by shear flows. Part 4. J. Fluid Mech. 13, 433448.Google Scholar
Miles, J. W. 1993 Surface-wave generation revisited. J. Fluid Mech. 256, 427441.Google Scholar
Mitsuyasu, H., Tasai, F., Suhara, T. et al. 1975 Observations of the directional spectrum of ocean waves using a cloverleaf buoy. J. Phys. Oceanogr. 5, 750760.Google Scholar
Morland, L. C. & Saffman, P. G. 1993 Effect of wind profile on the instability of wind blowing over water. J. Fluid Mech. 252, 383398.Google Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417445.Google Scholar
Phillips, O. M. 1958 On some properties of the spectrum of wind-generated ocean waves. J. Mar. Res. 16, 231245.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.
Phillips, O. M. 1988 Remote sensing of the sea surface. Ann. Rev. Fluid Mech. 20, 89109.Google Scholar
Snyder, R. L., Dobson, F. W., Elliott, J. A. & Long, R. B. 1981 Array measurements of atmospheric pressure fluctuations above surface gravity waves. J. Fluid Mech. 102, 159.Google Scholar
Valenzuela, G. R. 1976 The growth of gravity-capillary waves in a coupled shear flow. J. Fluid Mech. 76, 229250.Google Scholar
Young, I. R., Verhagen, L. A. & Banner, M. L. 1995 A note on the bimodal directional spreading of fetch-limited wind waves. J. Geophys. Res. 100 (C1), 773778.Google Scholar
Zakharov, V. E. & Shrira, V. I. 1990 Formation of the angular spectrum of wind waves. Sov. Phys. JETP 71, No. 6, 10911100.Google Scholar