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Viscous effects on wave generation by strong winds

Published online by Cambridge University Press:  01 February 2008

A. ZEISEL ,
M. STIASSNIE  and
Y. AGNON
A. ZEISEL
Affiliation:
Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
M. STIASSNIE
Affiliation:
Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Y. AGNON
Affiliation:
Department of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
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Abstract

This paper deals with the stability of water waves in a shear flow. Both temporal and spatial growth rates are derived. A carefully designed numerical solver enables us to extend the range of previous calculations, and to obtain results for larger wavelengths (up to 20 cm) and stronger winds (up to a friction-velocity of 1 m s−1). The main finding is the appearance of a second unstable mode which often turns out to be the dominant one. A comparison between results from the viscous model (Orr–Sommerfeld equations) and those of the inviscid model (Rayleigh equations), for 18 cm long waves, reveals some similarity in the structure of the eigenfunctions, but a significant difference in the imaginary part of the eigenvalues (i.e. the growth rate). It is found that the growth rate for the viscous model is 10 fold larger than that of the inviscid one.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 597 , 25 February 2008 , pp. 343 - 369
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.Google Scholar
Boomkamp, P. A. M., Boersma, B. J., Miesen, R. H. M. & Beijnon, G. V. 1997 Chebyshev collocation method for solving two-phase flow stability problem. J. Comput. Phys. 132, 191–200.CrossRefGoogle Scholar
Caulliez, G., Ricci, N. & Dupont, R. 1998 The generation of the first visible wind waves. Phys. Fluids Lett. 10, 757–759.CrossRefGoogle Scholar
Charnock, H. 1955 Wind stress on water surface. Q. J. R. Met. Soc. 81, 639–640.CrossRefGoogle Scholar
Jeffreys, H. 1925 On the formation of water waves by wind. Proc. R. Soc. A 104, 189–206.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.CrossRefGoogle Scholar
Larson, T. R. & Wright, J. W. 1974 Wind-generated gravity capillary waves: laboratory measurements of temporal growth rates using microwave backscatter. J. Fluid Mech. 70, 417–436.CrossRefGoogle Scholar
Miles, J. W. 1957 a On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185–204.CrossRefGoogle Scholar
Miles, J. W. 1957 b On the velocity profile for turbulent flow near a smooth wall. J. Aero. Sci. 24, 704.Google Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445.CrossRefGoogle Scholar
Powell, M. D., Vickery, P. J. & Rienhold, T. A. 2003 Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 422, 279–283.CrossRefGoogle ScholarPubMed
Stiassnie, M., Agnon, Y. & Janssen, P. A. E. M. 2007 Temporal and spatial growth of wind waves. J. Phys. Oceanogr. 37, 106–114.CrossRefGoogle Scholar
Trefethen, L. N. 2000 Spectral Methods in MATLAB. SIAM.CrossRefGoogle Scholar
Tsai, W. T. & Lin, M. Y. 2004 Stability analysis on the initial surface-wave generation within an air-sea coupled shear flow. J. Mar. Sci. Technol. 12, 200–208.CrossRefGoogle Scholar
Tsai, Y. S., Grass, A. J. & Simons, R. R. 2005 On the spatial linear growth of gravity–capillary water waves sheared by a laminar air flow. Phys. Fluids 17, 095101-1–095101-13.Google Scholar
Valenzuela, G. R. 1976 The growth of gravity-capillary waves in a coupled shear flow. J. Fluid Mech. 76, 229–250.CrossRefGoogle Scholar
Vallee, O. & Soares, M. 2004 Airy Functions and Application to Physics. Imperial College Press.CrossRefGoogle Scholar
VanGastel, K. Gastel, K., Janssen, P. A. E. M. & Komen, G. J. 1985 On phase velocity and growth rate of wind-induced gravity-capillary waves. J. Fluid Mech. 161, 199–216.Google Scholar
Wheless, G. H. & Csanady, G. T. 1993 Instability waves on the air–sea interface. J. Fluid Mech. 248, 363–381.CrossRefGoogle Scholar
Zhang, X. 2005 Short surface waves on surface shear. J. Fluid Mech. 541, 345–370.CrossRefGoogle Scholar
Zhang, X. & Harrison, S. 2004 A laboratory observation of the surface temperature and velocity distributions on a wavy and windy airwater interface. Phys. Fluids 16 (1), L5–L8.CrossRefGoogle Scholar