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A Numerical Study of Solitary Wave Interactions with a Bottom Step

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Continuous and Distributed Systems II

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 30))

Abstract

The numerical scheme for simulation of viscous nonlinear interactions between a solitary wave and a nonregular bottom is developed. It combines the boundary integral method for description of free-surface deformations, conformal mapping used to satisfy the nonleaking boundary condition on the bottom and the vortex method for integrating the fluid dynamic equations. A series of simulations were performed to study free-surface transformations and vortical flow patterns when propagating the solitary wave over a submerged step. Types of both the reflected and transmitted waves are shown to depend on the ratio of the incident wave amplitude to the water depth over the top step wall. The obtained critical value of this coefficient, at which the transmitted wave will be always breaking, is about 0.8 that is in congruence with the experimental data. The detailed investigation of the vortical patterns generated by a solitary wave near the step edge detected two large opposite vortices shedding in both the upstream and downstream directions. Interaction of those specifies the fluid dynamics and turbulent processes in the region.

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Authors and Affiliations

  1. Institute of Hydromechanics, National Academy of Sciences of Ukraine, Zheliabova St. 8/4, Kyiv, 03680, Ukraine

    I. M. Gorban

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  1. I. M. Gorban
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Correspondence to I. M. Gorban .

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Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Viktor A. Sadovnichiy

  2. Kiev Polytechnic Institute, National Technical University Ukraine, Kiev, Ukraine

    Mikhail Z. Zgurovsky

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Gorban, I.M. (2015). A Numerical Study of Solitary Wave Interactions with a Bottom Step. In: Sadovnichiy, V., Zgurovsky, M. (eds) Continuous and Distributed Systems II. Studies in Systems, Decision and Control, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-19075-4_22

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  • DOI: https://doi.org/10.1007/978-3-319-19075-4_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19074-7

  • Online ISBN: 978-3-319-19075-4

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