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Models for very wide-angle water waves and wave diffraction

  • Robert A. Dalrymple (a1) and James T. Kirby (a2)

Abstract

For a bathymetry consisting of parallel bottom contours, wide-angle parabolic models are developed to describe the diffraction of linear water waves. The first model, developed by operator correspondence, extends the validity of conventional forms of the parabolic model for wave angles up to 70° from the assumed wave direction. Through the use of Fourier decomposition, wave models valid to 90° are developed for three different lateral boundary conditions. By application, it is shown that the diffraction of waves through gaps or around structures is governed by the initial wave condition at the structure, which can be expanded into progressive and evanescent wave modes. Away from the structure, the wave field consists of only the progressive wave modes, which disperse according to their direction of propagation, the water depth and Snell's Law. Examples are shown for oblique waves through a gap, directional seas past a breakwater, a plane wave with varying crest amplitude, and finally for the diffraction of waves into a channel.

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Baker, B. B. & Copson E. T. 1950 The Mathematical Theory of Huygen's Principle, 2nd edn. Oxford University Press, 192 pp.
Battjes J. A. 1968 Refraction of water waves J. Waterways Harbors Div., ASCE, 94 (WW4), 437451.
Berkhoff J. C. W. 1972 Computation of combined refraction-diffraction. Proc. 13th Intl Conf. Coastal Engng, ASCE, Vancouver, pp. 471490.
Biesel F. 1964 Equations approchées de la réfraction de la houle. Proc. 9th Intl Conf. Coastal Engng, ASCE, Lisbon, pp. 5569.
Booij N. 1981 Gravity waves on water with non-uniform depth and current. Rep. 81–1. Dept of Civil Eng., Delft University of Technology.
Booij N. 1983 A note on the accuracy of the mild-slope equation. Coastal Engng 7, 191203.
Booker, H. G. & Clemmow P. C. 1950 The concept of an angular spectrum of plane waves, and its relation to that of polar diagram and aperture distribution Proc. Inst. Elect. Engrs. Part III, 97, 1117.
Claerbout F. 1985 Fundamentals of Geophysical Data Processing, with Application to Petroleum Prospecting. Palo Alto: Blackwell Scientific, 274 pp.
Dalrymple, R. A. & Greenberg M. 1985 Directional wavemakers. In Physical Modelling in Coastal Engineering (ed. R. A. Dalrymple). A. A. Balkema.
Dean, R. G. & Dalrymple R. A. 1984 Water Wave Mechanics for Engineers and Scientists. Englewood Cliffs: Prentice-Hall, 353 pp.
Dingemans M. W. 1983 Verification of numerical wave propagation models with field measurements. CREDIZ verification Haringvliet. Rep. W488, pt. 1. Delft Hydraul. Lab., Delft.
Kirby J. T. 1986a Higher-order approximations in the parabolic equation method for water waves. J. Geophys. Res. 91, 933952.
Kirby J. T. 1986b Rational approximations in the parabolic equation method for water waves Coastal Engng, 10, 355378.
Kirby, J. T. & Dalrymple R. A. 1983 A parabolic equation for the combined refraction-diffraction of Stokes waves by mildly varying topography. J. Fluid Mech. 136, 453466.
Kirby, J. T. & Dalrymple R. A. 1984 Verification of a parabolic equation for propagation of weakly-nonlinear waves Coastal Engng, 8, 219232.
Kirby, J. T. & Dalrymple R. A. 1986 Modeling waves in surfzones and around islands J. Waterway, Port, Coastal Ocean Engng, ASCE, 112, 7893.
Lee J.-J. 1971 Wave induced oscillations in harbours of arbitrary geometry. J. Fluid Mech. 45, 375394.
Liu, P. L.-F. & Tsay T. K. 1984 Refraction-diffraction model for weakly nonlinear water waves. J. Fluid Mech. 141, 265274.
Madsen O. S. 1974 A three dimensional wavemaker, its theory and application J. Hydraulic Res., 12, 205222.
McAninch G. L. 1986 Higher order parabolic approximations for sound propagation in stratified moving media. AIAA J. 24, 2.
Mei C. C. 1983 The Applied Dynamics of Ocean Surface Waves. Wiley-Interscience, 740 pp.
Mei C. C., Tlapa, G. A. & Eagleson P. S. 1968 An asymptotic theory for water waves on beaches of mild slope. J. Geophys. Res. 73, 45554560.
Mei, C. C. & Tuck E. O. 1980 Forward scattering by long thin bodies. SIAM J. Appl. Maths 39, 178191.
Penney, W. G. & Price A. T. 1952 The diffraction theory of seawaves and the sheltering afforded by a breakwater Phil. Trans. R. Soc. Lond. A 244, 236253.
Radder A. C. 1979 On the parabolic equation method for water-wave propagation. J. Fluid Mech. 95, 159176.
Stamnes J. J. 1986 Waves in Focal Regions. Bristol: Adam Hilger, 600 pp.
Stamnes J. J., Lovhaugen O., Spjelkavik B., Mei C. C., Lo, E. & Yue D. K. P. 1983 Nonlinear focusing of surface waves by a lens-theory and experiment. J. Fluid Mech. 135, 7194.
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Models for very wide-angle water waves and wave diffraction

  • Robert A. Dalrymple (a1) and James T. Kirby (a2)

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