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Nonlinear energy transfer in gravity–capillary wave spectra, with applications

Published online by Cambridge University Press:  29 March 2006

G. R. Valenzuela  and
M. B. Laing
G. R. Valenzuela
Affiliation:
Naval Research Laboratory, Washington, D.C.
M. B. Laing
Affiliation:
Naval Research Laboratory, Washington, D.C.
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Abstract

The energy flux in gravity-capillary wave spectra has been obtained using Hasselmann's (1962) perturbation analysis for a homogeneous Gaussian sea. As expected, resonant interactions now appear at second order, and a third-order perturbation analysis shows that energy is redistributed from waves with intermediate wavelengths (in the neighbourhood of 1·7 cm) toward gravity and capillary waves. Numerical computations are also obtained for the energy flux and the interaction time of a sharply peaked spectrum consisting of wavenumbers concentrated around a single wavenumber, superposed on a smooth background spectrum. The range of validity of the inviscid results is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 3 , 8 August 1972 , pp. 507 - 520
Copyright
© 1972 Cambridge University Press

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References

Benney, D. J. 1962 J. Fluid Mech. 14, 577–584.
Cox, C. X. 1958 J. Mar. Res. 16, 199–225.
Hasselmann, K. 1962 J. Fluid Mech. 12, 481–500.
Hasselmann, K. 1963a J. Fluid Mech. 15, 273–281.
Hasselmann, K. 1963a J. Fluid Mech. 15, 385–398.
Hasselmann, K. 1966 Rev. Geophys. 4, 1–32.
Hasselmann, K. 1968 Basic Developments in Fluid Dynamics (ed. M. Holt), pp. 117–182. Academic.
Longuet-Higgins, M. S. 1962 J. Fluid Mech. 12, 321–332.
McGoldrick, L. F. 1965 J. Fluid Mech. 21, 305–331.
McGoldrick, L. F. 1970 J. Fluid Mech. 40, 251–271.
Phillips, O. M. 1957 J. Fluid Mech. 2, 417–445.
Phillips, O. M. 1960 J. Fluid Mech. 9, 193–217.
Pierson, W. J. & Fife, P. 1961 J. Geophys. Res. 66, 163–179.
Simmons, W. F. 1969 Proc. Roy. Soc A 309, 551–575.
Valenzuela, G. R., Laing, M. B. & Daley, J. C. 1971 J. Mar. Res. 29, 69–84.
Wright, J. W. & Keller, W. C. 1971 Phys. Fluids, 14, 466–474.