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Nonlinear Wave Deformation on a Beach with Arbitrary Profile

  • K. Nadaoka
  • M. Hino
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

A new wave equation has been derived for fully nonlinear dispersive waves propagating over an arbitrarily shaped sea bed. The method of the derivation of the equation uses a conformal mapping technique by which the original domain can be transformed onto a uniform depth region to make the basic equation easily integrable vertically. By taking an inverse Fourier transform, the velocity potential obtained by the integration can be expressed in the form which can construct the exact wave equation from the water surface boundary conditions. An example of the numerical solution is presented to demonstrate the availability of the proposed wave equation. Further, for practical use, a WKB approximate solution is also presented.

Keywords

Wave Equation Conformal Mapping Inverse Fourier Transform Original Domain Conformal Mapping Technique 
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References

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    Mei, C.C.: The Applied Dynamics of Ocean Surface Waves, John & Wiley Sons, Inc., New York 1983.MATHGoogle Scholar
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    Fenton, J.D.; Rienecker, M.M.: Accurate numerical solutions for nonlinear waves, Proc. 17th Int. Conf. on Coastal Eng., ASCE, (1980) 50–69.Google Scholar
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    Hamanaka, K. Kato, K.: Perturbation analysis of finite amplitude waves with slowly varying depth, Proc. 29th Japanese Conf. on Coastal Eng., JSCE, (1982) 65–69 (in Japanese).Google Scholar
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    Nadaoka, K.; Hino, M.: Conformal mapping solution of a wave field on the arbitrarily shaped sea bed, Proc. 19th Conf. on Coastal Eng., ASCE, (1984) 1192–1208.Google Scholar
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    Nadaoka, K.: A fundamental study on shoaling and velocity field structure of water waves in the nearshore zone, Doctoral Dissertation, Tokyo Inst. of Tech. 1986. (reproduced in Tech. Rept. of Dept. Civil Eng., Tokyo Inst. of Tech., 36, (1986) 33–125 ).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • K. Nadaoka
    • 1
  • M. Hino
    • 1
  1. 1.Dept. of Civil Eng.Tokyo Institute of TechnologyJapan

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