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Asymptotic Behavior of a Shallow-Water Soliton Reflected at a Sloping Beach

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Summary

This paper deals with a long-time asymptotic behavior of a shallow water soliton reflected at a sloping beach. Based on the edge-layer theory, it is shown that the boundary-value problem for the Boussinesq equation under the “reduced” boundary condition is simplified to an “initial value” problem for the Korteweg-de Vries equation in the form of the spatial evolution of the reflected wave. Solving it numerically, the asymptotic behavior is demonstrated and compared with the one which evolves from the “initial value” obtained by solving the full nearshore behavior by the boundary element method.

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References

  1. Sugimoto, N.; Kakutani, T.: Reflection of a shallow-water soli-ton. Part 1. Edge-layer theory for shallow-water waves. J. Fluid Mech. 146 (1984) 369–382.

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  2. Sugimoto, N.; Kusaka, Y.; Kakutani, T.: Reflection of a shallow-water soliton. Part 2. Numerical evaluation. J. Fluid Mech. 178 (1987) 99–117.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan

    N. Sugimoto & T. Kakutani

Authors
  1. N. Sugimoto
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  2. T. Kakutani
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Editor information

Editors and Affiliations

  1. Dept. of Civil Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

    Kiyoshi Horikawa

  2. Dept. of Naval Architecture and Ocean Engineering, Yokohama National University, 156 Tokiwadai, Hodogaya-ku, Yokohama 240, Japan

    Hajime Maruo

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© 1988 Springer-Verlag Berlin Heidelberg

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Sugimoto, N., Kakutani, T. (1988). Asymptotic Behavior of a Shallow-Water Soliton Reflected at a Sloping Beach. In: Horikawa, K., Maruo, H. (eds) Nonlinear Water Waves. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83331-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-83331-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83333-5

  • Online ISBN: 978-3-642-83331-1

  • eBook Packages: Springer Book Archive

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