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On the mass and momentum transfer between short gravity waves and larger-scale motions

Published online by Cambridge University Press:  29 March 2006

K. Hasselmann
K. Hasselmann
Affiliation:
Institut für Geophysik, Universität Hamburg Present address: Woods Hole Oceanographic Institution.
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Abstract

Interactions between short gravity waves and larger-scale flows are investigated in the two-scale approximation. The effect of the wave field on the mean flow is described by an interaction stress tensor and a surface mass transfer. The results are applied to Phillips’ and Longuet-Higgins’ model of short waves breaking on the crests of long carrier waves. It is found that the work done on the long waves by the interaction stresses (corresponding to Longuet-Higgins’ ‘maser’ mechanism of wave generation) is almost exactly balanced by the loss of potential energy arising from the mass transfer. The residual energy transfer leads to attenuation of the long waves, independent of their propagation direction relative to the short waves. Damping factors are estimated from the upwind–downwind ratios of radar backscatter cross-sections. It is found that interactions with waves shorter than 35cm yield attenuation rates about an order of magnitude smaller than the observed growth rates due to the wind.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 1 , 15 November 1971 , pp. 189 - 205
Copyright
© 1971 Cambridge University Press

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References

Barnett, T. P. & Wilkerson, J. C. 1967 On the generation of wind waves as inferred from airborne radar measurements of fetch-limited spectra. J. Mar. Res. 25, 292–328.Google Scholar
Bisshopp, F. E. 1969 Nonlinear wave propagation in the geometrical approximation. Div. Appl. Math., Brown Univ. Tech. Rep. no. 9.Google Scholar
Bretherton, F. P. & Garrett, C. J. R. 1968 Wave trains in inhomogeneous moving media. Proc. Roy. Soc. A 302, 529–554.Google Scholar
Daley, J. C. 1966a Sea clutter measurements at X and C band. Nav. Res. Lab. Rep.Google Scholar
Daley, J. C. 1966b Airborne radar backscatter study at four frequencies. Nav. Res. Lab. Rep.Google Scholar
Hasselmann, K. 1962 On the nonlinear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481–500.Google Scholar
Hasselmann, K. 1970 Wave-driven inertial oscillations. Geophys. Fluid Dyn. 1, 463–502.Google Scholar
Hasselmann, K., Munk, W. H. & MacDonald, G. J. F. 1963 Bispectra of ocean waves. In Time Series Analysis (ed. M. Rosenblatt), ch. 8. Wiley.
Hasselmann, K. & Schieler, M. 1970 Doppler spectra of electromagnetic backscatter from the sea surface at centimeter-decimeter and decameter wavelengths. Proc. Eighth Naval Hydrodyn. Conf., Pasadena (in the Press).
Longuet-Higgins, M. S. 1969a A nonlinear mechanism for the generation of sea waves. Proc. R. Soc. A 311, 371-389.
Longuet-Higgins, M. S. 1969b Action of a variable stress at the surface of water waves. Phys. Fluids, 12, 737-740.
Longuet-Higgins, M. S. & Stewart, R. W. 1960 Changes in the form of short gravity waves on long waves and tidal currents. J. Fluid Mech. 8, 565–583.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1961 The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10, 529–549.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stresses in water waves; a physical discussion, with applications. Deep-Sea Res. 11, 529–562.Google Scholar
Marks, W. 1965 The application of airborne radar backscatter to measurement of the state of sea. In Oceanography from Space (ed. G. Ewing), pp. 377–391. Woods Hole Oceanographic Inst.
Peake, W. H. 1959 Theory of radar return from Terrain. IRE Nat. Conv. Rec. 7, 27–41.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of kite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193–217.Google Scholar
Phillips, O. M. 1963 On the attenuation of long gravity waves by short breaking waves. J. Fluid Mech. 16, 321–332.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Rice, S. O. 1951 Reflection of electromagnetic waves from slightly rough surfaces. Comm. Pure Appl. Math. 4, 351–378.Google Scholar
Snodgrass, F. E., Groves, G. W., Hasselmann, K. F., Miller, G. R., Munk, W. H. & Powers, W. H. 1966 Propagation of ocean swell across the Pacific. Phil. Trans. A 259, 431–497.Google 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
Valenzuela, G. R. 1968 Scattering of electromagnetic waves from a tilted slightly-rough surface. Radio Science, 3, 1057–1066.Google Scholar
Valenzuela, G. R. & Laing, M. B. 1970 Study of Doppler spectra of radar sea echo. J. Geophys. Res. 75, 551–563.Google Scholar
Whitham, G. B. 1967 Variational methods and applications to water waves. Proc. Roy. Soc. A 299, 6–25.Google Scholar
Wright, J. W. 1968 A new model for sea clutter. IEEE Trans. AP-16, 217–223.