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On the reflexion of wave characteristics from rough surfaces

Published online by Cambridge University Press:  29 March 2006

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
Oregon State University, Corvallis
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Abstract

The energy of internal waves tends to be propagated along certain characteristic paths inclined at fixed angles to the vertical direction; the angle of inclination depending only on the wave frequency and the density stratification (not on the wavelength). The reflexion of such waves by smooth plane surfaces has been discussed recently by Sandstrom (1966).

In the present paper the role of surface roughness is examined. Surprisingly, it appears that quite small-scale irregularities can completely alter the reflecting properties of a surface; the tangential scale of the roughness elements may be much smaller than the wavelength of the incident or reflected waves. All scales of roughness are relevant, down to those comparable in magnitude to the thickness of the oscillatory boundary layer. For tidal waves in the ocean this thickness is of the order of 1 m.

The behaviour of the coefficient of transmission as a function of the angle of incidence appears at first sight to be extremely complicated. Some simple examples of periodic surface roughnesses are discussed and elucidated: a sawtooth, a square-topped wave and a simple sine-wave. The transmission coefficient T for a sine-wave, for example, is shown in figure 9. An approximate expression for T is also derived in the case of a slowly modulated sine-wave (figure 10). These results are for a non-viscous fluid. The effects of viscosity are also considered qualitatively.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 2 , 23 June 1969 , pp. 231 - 250
Copyright
© 1969 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
Bole, J. B. & Hsu, E. Y. 1967 Response of gravity water waves to wind excitation. Stanford Univ. Civil Engrg. Dept. Tech. Rep. no. 79.Google Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer J. Fluid Mech. 1, 191–226.Google Scholar
Conte, S. D. & Miles, J. W. 1959 On the numerical integration of the Orr-Sommerfeld equation J. Soc. Indust. Appl. Math. 7, 361–6.Google Scholar
Dean, R. G. 1965 Stream function representation of nonlinear ocean waves J. Geophys. Res. 70, 4561–72.Google Scholar
Hamada, T. 1963 An experimental study of development of wind waves. Port and Harbour Tech. Res. Inst. Rep. no. 2, Yokosuka, Japan.Google Scholar
Hsu, E. Y. 1965 A wind, water-wave research facility. Stanford Univ. Engrg. Dept. Tech. Rep. no. 57.Google Scholar
Hunt, J. N. 1952 Viscous damping of waves over an inclined bed in a channel of finite width Houille Blanche, 7, 836.Google Scholar
Inoue, T. 1966 On the growth of the spectrum of a wind generated sea according to a modified Miles-Philiips mechanism. New York Univ. Dept of Met. and Ocean., Geophys. Sci. Lab. Rep. no. TR66-6.Google Scholar
Jeffreys, H. 1925 On the formation of water waves by wind. Proc. Roy. Soc A 107, 189–206.Google Scholar
Korwin-Kroukovsky, B. V. 1966 Air pressures causing wave development, estimate by theory, model tests, and observations Dt. hydrogr. Z. 19, 145–59.Google Scholar
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind J. Fluid Mech. 14, 385–98.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows J. Fluid Mech. 3, 185–204.Google Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows J. Fluid Mech. 6, 568–82.Google Scholar
Miles, J. W. 1967 On the generation of surface waves by shear flows. Part 5 J. Fluid Mech. 20, 163–75.Google Scholar
Phillips, O. M. 1958 Wave generation by turbulent wind over a finite fetch. Proc. 3rd Natn. Congr. Appl. Mech. pp. 785–9.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Shemdin, O. H. 1968 Wind generated waves: recent and future developments. Fifth Space Congress, Oceanography Session, Cocoa Beach, Florida.
Shemdin, O. H. & Hsu, E. Y. 1966 The dynamics of wind in the vicinity of progressive water waves. Stanford Univ. Civil Engrg. Dept. Tech. Rep. no. 66.Google Scholar
Shemdin, O. H. & Hsu, E. Y. 1967 Direct measurement of aerodynamic pressure above a simple progressive gravity wave J. Fluid Mech. 30, 403–16.Google Scholar
Snyder, R. L. & Cox, C. S. 1966 A field study of the wind generation of ocean waves J. Mar. Res. 24, 141–78.Google Scholar
Wiegel, R. L. & Cross, R. H. 1966 Generation of wind waves J. WatWays Harb. Div. ASCE 92, 1–26.Google Scholar