Modulation of Short Wind Waves by Long Waves
The behavior of short surface waves (wavelength less than a meter or so) riding on longer wind waves or swell has sparked interest for several decades now. In the problem as posed here, the energetic waves near the peak of a wind-wave or swell spectrum are treated as a large-scale, slowly varying “medium” in which short gravity-capillary waves evolve. This “WKB approximation” should be well founded, since the time and space scales of the long and short waves are widely separated, and no reflections of the short waves occur. Short wave “packets” or “components” are examined independently as they evolve under the influence of slowly varying winds and currents, and later reassembled into a larger picture. Resonant non-linear exchanges are not explicitly included, although (for example) a “packet” might be regarded as a set of tightly coupled wavenumbers rather than as a pure sine-wave component.
Unable to display preview. Download preview PDF.
- Abramowitz, M., and I. Stegun, 1965: Handbook of Mathematical Functions, Dover.Google Scholar
- Bretherton, F.P. and C.J.R. Garrett, 1969: Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. A302, 529.Google Scholar
- Cox, C.S., 1958: Measurements of slopes of high-frequency wind waves. J. Mar. Res. 16, 199–225.Google Scholar
- Garrett, C., 1976: Generation of Langmuir circulations by surface waves — a feedback mechanism J. Mar. Res. 34, 117–130.Google Scholar
- Hasse, L., 1986: On Charnock’s relation for roughness at sea Oceanic Whitecaps and their role in air-sea exchange processes. E.C. Monahan and G. Mac-Niocaill, eds.Google Scholar
- Henyey, F.S., D.B. Creamer, K.B. Dysthe, R.L., and J.A. Wright, 1988: The energy and action of small waves riding on large waves, (submitted to J. Fluid Mech.)Google Scholar
- Landahl, M.T., J.A. Smith, and S.E. Widnall, 1986: The interaction between long and short wind-generated waves in Wave Dynamics and Radio Probing of the Ocean Surface, (eds. O.M. Phillips and Klaus Hasselmann) 59–47.Google Scholar
- Longuet-Higgins, M.S., 1969a: On wave breaking and the equilibrium spectrum of wind generated waves. Proc. Roy. Soc, A311, 371–389.Google Scholar
- Phillips, O.M., 1977: The dynamics of the upper ocean. (2nd ed.) Cambridge University Press, 336pp.Google Scholar
- Smith, J.A., 1980: Waves, currents, and Langmuir circulation. Ph.B. Thesis, Dept. of Oceanography. Dalhousie University Nova Scotia, Canada.Google Scholar
- Stewart, R.H. and J.W. Joy, 1974: HF radio measurements of surface currents. Deep-Sea Research, 21, 1039–1049.Google Scholar
- Tennekes, H. and J.L. Lumley, 1972: A First Course in Turbulence. MIT Press, 300pp.Google Scholar
- Whitham, G.E., 1974 Linear and Nonlinear Waves, Wiley, N.Y.Google Scholar