Abstract
Generation and growth of gravity-capillary waves (λ ~ 1 cm) by wind is reconsidered. Our main objective is to establish the sensitivity of this process to strength and profile of wind and wind-induced shear current. To this end we give a quasi-analytical description of the process based on linear instability theory. We start from a coupled wind-current system and solve the equations by expansion in the small parameters ρa/ρw, 1/Ra and 1/Rw. The solutions are valid for all friction velocities. We indicate where our work extends earlier results of Brooke-Benjamin (1959), Miles (1962), Valenzuela (1976) and Kawai (1979). We find that the phase velocity is mainly sensitive to the current profile and the growth rate to the wind profile. The growth rate of the initial wavelets, the first waves to be generated, scales with the friction velocity u*, as u 3* .
Extended Abstract. A full account is given by van Gastel, Janssen and Komen, 1984.
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References
Brooke Benjamin, T., 1959. Shearing flow over a wavy boundary, J. of Fluid Mech., 6, pp. 161–205.
Drazin, P.G. Reid, W.H., 1982. Hydrodynamic Stability, Cambridge University Press, Cambridge.
Gastel, K. van, Janssen, P.A.E.M. Komen, G.J., 1984. On Phase Velocity and Growth Rate of Wind-Induced Gravity-Capillary Waves. J. of Fluid Mech., to appear.
Janssen, P.A.E.M. Peeck, H.H., 1984. On the quasilinear evolution of the coupled air-flow, water wave system. Submitted for Publication.
Kawai, S., 1979. Generation of Initial Wavelets by Instability of a Coupled Shear Flow and their Evolution to Wind Waves, J. of Fluid Mech., 93, pp. 661–703.
Larson, T.R. Wright, J.W., 1975. Wind-generated gravity capillary waves: laboratory measurements of temporal growth rates using microwave backscatter, J. of Fluid Mech., 70, pp. 417–436.
Miles, J.W., 1957. On the Generation of Surface Waves by Shear Flows, J. of Fluid Mech., 3, pp. 185–204.
Miles, J.W., 1962. On the generation of surface waves by shear flows. Part 4, J. of Fluid Mech., 13, pp. 433–448.
Schroeder, L.C., Boggs, D.H., Dome, G., Halberstam, I.M., Jones, W.L., Pierson, W.J. Wentz, F.J., 1982. The Relationship Between Wind Vector and Normalized Radar Cross Section Used to Derive SEASAT-A Satellite Scatterometer Winds, J. of Geophysical Research, 87, pp. 3318–3336.
Valenzuela, G.R., 1976. The Growth of Gravity-Capillary Waves in the Coupled Shear Flow, J. of Fluid Mech., 76, pp. 229–250.
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van Gastel, K., Janssen, P.A.E.M., Komen, G.J. (1985). On the Growth of Gravity-Capillary Waves by Wind. In: Toba, Y., Mitsuyasu, H. (eds) The Ocean Surface. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7717-5_9
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DOI: https://doi.org/10.1007/978-94-015-7717-5_9
Publisher Name: Springer, Dordrecht
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