Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-17T14:28:17.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of wind profile on the instability of wind blowing over water

Published online by Cambridge University Press:  26 April 2006

L. C. Morland  and
P. G. Saffman
L. C. Morland
Affiliation:
Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
P. G. Saffman
Affiliation:
Department of Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A linear stability analysis of the inviscid, parallel flow of air over water leads to an eigenvalue problem for the wave speed, which is solved numerically for air profiles typical of both laminar and turbulent flows. Comparison is made with Miles’ (1957) theory; growth rates differ from those predicted from the Miles (1957) formula but are in agreement with Conte & Miles’ (1959) computations for turbulent flow profiles. In the limit of a highly sheared wind profile the numerical computations retrieve the Kelvin-Helmholtz instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 383 - 398
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

With an Appendix by J. W. Miles

References

Akylas, T. R. 1982 A nonlinear theory for the generation of water waves by wind. Stud. Appl. Maths 67, 1–24.Google Scholar
Barnett, T. P. & Wilkerson, J. C. 1967 On the generation of ocean wind waves as inferred from airborne radar measurements of fetch-limited spectra. J. Mar. Res. 25, 292–321.Google Scholar
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech 6, 161–205.Google Scholar
Chandrasekhar, S. 1970 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Conte, S. D. & Miles, J. W. 1959 On the numerical integration of the Orr-Sommerfeld equation. J. Soc. Indust. Appl. Maths 7, 361–366.Google Scholar
Dobson, F. W. 1971 Measurements of atmospheric pressure on wind-generated sea waves. J. Fluid Mech. 48, 91–127.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Duin, C. A. van & Janssen, A. E. M. 1992 An analytic model of the generation of surface gravity waves by turbulent air flow. J. Fluid Mech. 236, 197–215.Google Scholar
Elliott, J. A. 1972 Microscale pressure fluctuations near waves being generated by the wind. J. Fluid Mech. 54, 427–448.Google Scholar
Gastel, K. van, Janssen, P. A. E. M. & Kamen, G. J. 1985 On phase velocity and growth rate of wind-induced gravity-capillary waves. J. Fluid Mech. 161, 199–216.Google Scholar
Hasselman, D. & Bösenberg, J. 1991 Field measurements of wave-induced pressure over wind-sea and swell. J. Fluid Mech. 230, 391–428.Google Scholar
Howard, L. N. 1961 Note on a paper of John W. Miles. J. Fluid Mech. 10, 509–512.Google Scholar
Hughes, T. H. & Reid, W. H. 1965 On the stability of the asymptotic suction boundary-layer profile. J. Fluid Mech. 23, 715–735.Google Scholar
Kahma, K. K. & Donelan, M. A. 1988 A laboratory study of the minimum wind speed for wind wave generation. J. Fluid Mech. 192, 339–364.Google Scholar
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14, 385–398.Google Scholar
Long, R. B. 1980 A parametrical model for the vertical structure of the induced atmospheric pressure field above a spectrum of surface gravity waves. J. Fluid Mech. 99, 163–183.Google Scholar
Makin, V. K. 1988 Numerical results on the structure of the sea wave-induced pressure field in the atmosphere. Morskoy Gidofizichesky Zh., No. 2, 50–54.Google Scholar
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, 569–582.Google Scholar
Miles, J. W. 1962a A note on the inviscid Orr-Sommerfeld equation. J. Fluid Mech. 13, 427–432.Google Scholar
Miles, J. W. 1962b On the generation of surface waves by shear flows. Part 4. J. Fluid Mech. 13, 433–448.Google Scholar
Morland, L. C., Saffman, P. G. & Yuen, H. C. 1991 Waves generated by shear layer instabilities. Proc. R. Soc. Lond. A 433, 441–450.Google Scholar
Shemdin, O. H. 1972 Wind-generated current and phase speed of wind waves. J. Phys. Oceanogr. 2, 411–419Google Scholar
Snyder, R. L. 1974 A field study of wave-induced pressure fluctuations above surface gravity waves. J. Mar. Res. 32, 497–529Google Scholar
Snyder, R. L. & Cox, C. S. 1966 A field study of the wind generation of ocean waves. J. Mar. Res. 24, 141–178.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, 1–59.Google Scholar
Squire, H. B. 1933 On the stability of three-dimensional disturbances of viscous flow between parallel walls. Proc. R. Soc. Lond. A 142, 621–628Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Valenzuela, G. R. 1976 The growth of gravity-capillary waves in a coupled shear flow. J. Fluid Mech. 76, 229–250.Google Scholar
Yih, C. S. 1972 Surface waves in flowing water. J. Fluid Mech. 51, 209–220.Google Scholar