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Wave Propagation and Diffraction pp 201–235Cite as

Propagation and Evolution of Transient Water Waves

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Part of the book series: Foundations of Engineering Mechanics ((FOUNDATIONS))

Abstract

This chapter deals with some aspects of the initial-boundary-value problems of the initiation, generation and propagation of tsunami waves. The generation of tsunami waves by bottom movements is considered. We formulate an appropriate initial-boundary-value problem and analyse the effect of the sharpness of vertical axisymmetric bottom disturbance and the disturbance duration on the generation of tsunami waves. The propagation of nonlinear waves on water and their evolution over a nonrigid elastic bottom are investigated. Some aspects and indeterminacy of the formulation of the initial-boundary-value problems dealing with the initiation and generation of tsunami waves are considered. We consider some typical types of tsunami waves that demonstrate the indeterminacy of their initiation in time because of the indeterminacy in the physical trigger mechanism of underwater earthquakes. Based on the three-dimensional formulation, evolution equations describing the propagation of nonlinear dispersive surface waves on water over a spatially inhomogeneous bottom are obtained with allowance for the bottom disturbances in time. We use the Laplace transform with respect to the time coordinate and the power series method with respect to the spatial coordinate to find a solution to the nonstationary problem of the diffraction of surface gravity waves by a radial bottom inhomogeneity that deviates from its initial position. The propagation and stability of nonlinear waves in a two-layer fluid with allowance for surface tension are analysed by the asymptotic method of multiscale expansions.

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Authors and Affiliations

  1. Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Igor T. Selezov

  2. Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Yuriy G. Kryvonos

  3. Institute of Physics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Ivan S. Gandzha

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  1. Igor T. Selezov
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  3. Ivan S. Gandzha
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Selezov, I.T., Kryvonos, Y.G., Gandzha, I.S. (2018). Propagation and Evolution of Transient Water Waves. In: Wave Propagation and Diffraction. Foundations of Engineering Mechanics. Springer, Singapore. https://doi.org/10.1007/978-981-10-4923-1_6

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