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A harbour theory for wind-generated waves based on ray methods

Published online by Cambridge University Press:  12 April 2006

Jesper Larsen
Jesper Larsen
Affiliation:
Laboratory of Applied Mathematical Physics, Technical University of Denmark, CopenhagenPresent address: The Institute of Mathematical Technology, Sommervej 7, DK 2920 Charlottenlund, Denmark.
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Abstract

In the paper we consider harbour oscillations excited by wind-generated gravity waves. The analysis is based on the fact that waves propagate along rays (wave orthogonals). In this way the elliptic boundary-value problem is turned into an initial-value problem along each ray. When a ray strikes the boundary (the harbour walls), reflected rays are produced in accordance with the law of reflexion. When a ray strikes an edge point of the boundary (e.g. the tip of a breakwater) diffracted rays are produced and emitted in all directions into the harbour. Algorithms for the tracing of incident, multiply reflected and singly diffracted rays as well as the computation of the field on each ray are presented. Attenuation mechanisms (e.g. partial reflexion), which limit the number of rays needed to compute the field, are included. Numerical examples for a rectangular and an actual harbour are given. A comparison between the results obtained by ray methods and finite difference methods is included.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 1 , 12 July 1978, pp. 143 - 158
Copyright
© 1978 Cambridge University Press

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References

Berkhoff, J. C. W. 1973 Computation of combined refraction–diffraction. Proc. 13th Coastal Engng Conf. July 1972, Vancouver, vol. 1, pp. 471–490. New York: A.S.C.E.
Blue, F. L. & Johnson, J. W. 1949 Diffraction of waves passing through a breakwater gap. Trans. Am. Geophys. Un. 30, 705–718.Google Scholar
Carr, J. H. 1952 Wave protection aspects of harbor design. Hydrodynamics Lab., Cal. Inst. Tech. Rep. E-11.Google Scholar
Chao, Y.-Y. 1971 An asymptotic evaluation of the wave field near a smooth caustic. J. Geophys. Res. 76, 7401–7408.Google Scholar
Christiansen, P. L. 1975 Diffraction of gravity waves by large islands. Proc. 14th Coastal Engng Conf. July 1974, Copenhagen, vol. 1, pp. 601–614. New York: A.S.C.E.
Christiansen, P. L. 1976 Diffraction of gravity waves by ray methods. Proc. Int. Symp. Waves on Varying Depth, July 1976, Canberra. (To be published.)
Goda, Y. & Abe, Y. 1968 Apparent coefficient of partial reflection of finite amplitude waves. Rep. Port and Harbour Res. Inst. no. 7, pp. 3–53.Google Scholar
Hurd, R. A. 1976 The Wiener–Hopf–Hilbert method for diffraction problems. Can. J. Phys. 54, 775–780.Google Scholar
Hwang, L.-S. & Tuck, E. O. 1970 On the oscillations of harbors of arbitrary shape. J. Fluid Mech 42, 447–464.Google Scholar
Ippen, A. T. (ed.) 1966 Estuary and Coastal Hydrodynamics. McGraw-Hill.
Ippen, A. T. & Goda, Y. 1963 Wave induced oscillations in harbors: the solution for a rectangular harbour connected to the open sea. Hydrodynamics Lab., M.I.T. Rep. no. 59.Google Scholar
Jonsson, I. G. 1975 The wave friction factor revisited. Inst. Hydrodyn. Hydraulic Engng (I.S.V.A.), Tech. Univ. Denmark, Prog. Rep. no. 37, pp. 3–8.Google Scholar
Keller, J. B. 1958 Surface waves on water of non-uniform depth. J. Fluid Mech. 4, 607–614.Google Scholar
Keller, J. B. 1962 Geometrical theory of diffraction. J. Optical Soc. Am. 52, 116–130.Google Scholar
Kouyoumjian, R. G. & Pathak, P. H. 1974 A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface. Proc. I.E.E.E. 62, 1448–1461.Google Scholar
Larsen, J. 1977a Computation of harbour oscillations by ray methods. Ph.D. thesis, Tech. Univ. Denmark (DCAMM Rep. S8).
Larsen, J. 1977b A ray-tracing algorithm. To appear.
Larsen, J. & Christiansen, P. L. 1975 Computations of harbor oscillations by ray methods. Proc. Symp. Modeling Techniques, Sept. 1975, SanFrancisco, vol. 2, pp. 888–906. New York: A.S.C.E.
Lee, J.-J. 1971 Wave-induced oscillations in harbours of arbitrary geometry. J. Fluid Mech. 45, 375–394.Google Scholar
Madsen, O. S. 1974 Wave transmission through porous structures. Proc. A.S.C.E., J. Waterways, Harbors & Coastal Engng Div. 100, 169–188.Google Scholar
Madsen, O. S. & White, S. M. 1976 Energy dissipation on a rough slope. Proc. A.S.C.E., J. Waterways, Harbors & Coastal Engng Div. 102, 31–48.Google Scholar
Malyughinetz, G. D. 1960 Das Sommerfeldsche Integral und die Lösung von Beugungsaufgaben in Winkelgebieten. Ann. Phys. 1, 107–122.Google Scholar
Mei, C. C. & Chen, H. S. 1975 Hybrid-element method for water waves. Proc. Symp. Modeling Techniques, Sept. 1975, San Francisco, vol. 1, pp. 63–81, New York: A.S.C.E.
Miche, M. 1951 Le pouvoir réfléchissant des ouvrages maritimes exposés à l'action de la houle. Annales des Ponts et Chaussées 121, 285–319.Google Scholar
Miles, J. W. & Munk, W. 1961 Harbor paradox. Proc. A.S.C.E., J. Waterways, Harbors and Coastal Engng Div. 87, 111–131.Google Scholar
Penney, W. G. & Price, A. T. 1944 Diffraction of water waves by breakwaters. Directorate of Miscellaneous Weapons Development, Technical History 26, Artificial Harbors, 3–4.
Shen, M. C. 1975 Ray method for surface waves on fluid of variable depth. SIAM Rev. 17. 38–56.Google Scholar
Shen, M. C., Meyer, R. E. & Keller, J. B. 1968 Spectra of water waves in channels and around islands. Phys. Fluids 11, 2289–2304.Google Scholar
Smith, R. & Sprinks, T. 1975 Scattering of surface waves by a conical island. J. Fluid Mech. 72, 373–384.Google Scholar
Sommerfeld, A. 1896 Mathematische Theorie der Diffraktion. Math. Ann. 47, 317–374.Google Scholar
ünlüata, ü. & Mei, C. C. 1973 Long wave excitation in harbours – an analytical study. Ralph M. Parsons Lab. Water Resources Hydrodynamics, M.I.T. Rep. no. 171.Google Scholar