Modulation of short waves by surface currents: A numerical solution

Modulation of short waves by surface currents subjected to wind input and breaking dissipation is investigated. The dissipation is expressed as a power law function of the action density. The solution is presented in the form of an integral equation, and the method of characteristics is applied to obtain numerical results. The numerical solution compares favorably with the relaxation theory when the surface current is weak, and it can be applied to a strong current condition, where the linear assumption used in the derivation of the relaxation theory is no longer valid. The modulation response to various wind and wave parameters, such as short-wave wavelength, surface wind stress, long-wave frequency and steepness, different dissipation functions, and interaction length or duration between long and short waves, are discussed.

[1]  Owen M. Phillips,et al.  On the Response of Short Ocean Wave Components at a Fixed Wavenumber to Ocean Current Variations , 1984 .

[2]  A. Gargett,et al.  On the interaction of surface and internal waves , 1972, Journal of Fluid Mechanics.

[3]  M. Longuet-Higgins,et al.  Changes in the form of short gravity waves on long waves and tidal currents , 1960, Journal of Fluid Mechanics.

[4]  William J. Plant,et al.  Ocean wave‐radar modulation transfer functions from the West Coast Experiment , 1980 .

[5]  W. Plant.  A two-scale model of short wind-generated waves and scatterometry , 1986 .

[6]  O. Phillips.  Spectral and statistical properties of the equilibrium range in wind-generated gravity waves , 1985, Journal of Fluid Mechanics.

[7]  W. Alpers.  Theory of radar imaging of internal waves , 1985 .

[8]  William J. Plant,et al.  Parametric dependence of ocean wave-radar modulation transfer functions , 1983 .

[9]  K. Hasselmann,et al.  The two-frequency microwave technique for measuring ocean-wave spectra from an airplane or satellite , 1978 .

[10]  R. E. Sterner,et al.  A comparison of measured surface wave spectral modulations with predictions from a wave-current interaction model , 1988 .

[11]  John W. Miles,et al.  On the stability of heterogeneous shear flows , 1961, Journal of Fluid Mechanics.

[12]  P. Hwang,et al.  Breaking of wind-generated waves: measurements and characteristics , 1989, Journal of Fluid Mechanics.

[13]  D. Thompson,et al.  Calculation of radar backscatter modulations from internal waves , 1988 .

[14]  J. Miles.  On the generation of surface waves by shear flows , 1957, Journal of Fluid Mechanics.

[15]  H. Davis.  Introduction to Nonlinear Differential and Integral Equations , 1964 .

[16]  John W. Miles,et al.  On the generation of surface waves by shear flows. Part 4 , 1962, Journal of Fluid Mechanics.

[17]  J. Wright,et al.  Microwave scattering and the straining of wind‐generated waves , 1975 .

[18]  D. Thompson,et al.  Intensity modulation in SAR images of internal waves , 1986, Nature.

[19]  B. Hughes.  The effect of internal waves on surface wind waves 2. Theoretical analysis , 1978 .

[20]  W. Alpers,et al.  A theory of the imaging mechanism of underwater bottom topography by real and synthetic aperture radar , 1984 .

[21]  F. Bretherton,et al.  Wavetrains in inhomogeneous moving media , 1968, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[22]  O. Phillips.  The dynamics of the upper ocean , 1966 .

[23]  B. Hughes.  On the interaction of surface and internal gravity waves: uniformly valid solution by extended stationary phase , 1976, Journal of Fluid Mechanics.

[24]  M. Longuet-Higgins,et al.  Theory of the almost-highest wave: the inner solution , 1977, Journal of Fluid Mechanics.

[25]  J. E. Lewis,et al.  On the interaction of internal waves and surface gravity waves , 1974, Journal of Fluid Mechanics.