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On weak reflection of water waves

Published online by Cambridge University Press:  20 April 2006

Philip L.-F. Liu  and
Ting-Kuei Tsay
Philip L.-F. Liu
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853
Ting-Kuei Tsay
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853
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Abstract

The weak reflection of monochromatic water waves is studied for the cases of slowly varying water depth. A coupled system of equations for the forward-scattering (transmitted) and the backward-scattering (reflected) wavefields are derived from the mild-slope equation (Smith & Sprinks 1975). Parabolic approximation is then used to simplify the equations for the diffraction factor. An iterative numerical scheme is proposed to compute the resulting equations. The scheme converges very quickly for the cases of weak reflection. The accuracy of the present approach is shown by comparing with numerical results obtained by a hybrid finite-element formulation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 131 , June 1983 , pp. 59 - 71
Copyright
© 1983 Cambridge University Press

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References

Berkhoff, J. C. W. 1972 Computation of combined refraction-diffraction. In Proc. 13th Coastal Engng Conf., vol. 2, pp. 471–490. ASCE.
Berkhoff, J. C. W., Booy, N. & Radder, A. C. 1982 Verification of numerical wave propagation models for simple harmonic linear waves Coastal Engng 6, 255–279.Google Scholar
Carrier, G. F. 1966 Gravity waves on water of variable depth J. Fluid Mech. 24, 641–659.Google Scholar
Chen, H. S. & Mei, C. C. 1974 Oscillations and wave forces in an offshore harbor. Tech. Rep. no. 190, Ralph M. Parsons Lab. for Water Resources and Hydrodynamics, Dept Civil Engng, M.I.T.Google Scholar
Corones, J. 1975 Bremmer series that correct parabolic approximations. J. Math. Anal. Applics 50, 361–372.Google Scholar
Fock, V. A. 1946 The field of a plane wave near the surface of a conducting body J. Phys. U.S.S.R. 10, 399–409.Google Scholar
Fock, V. A., 1960 Electromagnetic Diffraction and Propagation Problems. Macmillan.
Leontovitch, M. A. 1944 A method of solution of problems of electromagnetic wave propagation along the earth's surface Izv. Akad. Nauk S.S.S.R. 8, 16–22.Google Scholar
Liu, P. L.-F. & Mei, C. C. 1976 Water motion on a beach in the presence of a breakwater: 1. Waves. J. Geophys. Res. 81, 3079–3084.Google Scholar
Lozako, C. J. & Liu, P. L.-F. 1980 Refraction-diffraction model for linear surface gravity waves J. Fluid Mech. 101, 705–720.Google Scholar
Lozano, C. J. & Meyer, R. D. 1976 Leakage and response of waves trapped by round islands Phys. Fluids 19, 1075–1088.Google Scholar
Lundgren, H. 1976 Physics and mathematics of waves in coastal zones. In Proc. 15th Coastal Engng Conf., Hawaii, pp. 880–885. ASCE.
Mei, C. C. & Tuck, E. O. 1980 Forward scattering by long thin bodies SIAM J. Appl. Maths 39, 178–191.Google Scholar
Meyer, R. E. 1979 Surface wave reflection by underwater ridges J. Phys. Oceanogr. 9, 150–157.Google Scholar
Radder, A. C. 1979 On the parabolic equation method for water-wave propagation J. Fluid Mech. 95, 159–176.Google Scholar
Smith, R. & Sprinks, T. 1975 Scattering of surface waves by a conical island J. Fluid Mech. 72, 373–384.Google Scholar
Tappert, F. D. 1977 The parabolic approximation method. In Wave Propagation and Underwater Acoustics (ed. J. B. Keller & J. S. Papadakis), chap. V. Springer.
Tsay, T.-K. & Liu, P. L.-F. 1982 Numerical solution of water-wave refraction and diffraction problems in the parabolic approximation J. Geophys. Res. 87, 7932–7940.Google Scholar
Tsay, T.-K. & Liu, P. L.-F. 1983 A finite element model for wave refraction and diffraction J. Appl. Ocean Res. 5, 30–37.Google Scholar
Yue, D. K. P. & Mei, C. C. 1980 Forward diffraction of Stokes waves by a thin wedge J. Fluid Mech. 97, 33–52.Google Scholar