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Analytical Solutions for Tsunami Waves Generated by Submarine Landslides in Narrow Bays and Channels

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Abstract

Analytical theory of tsunami wave generation by submarine landslides is extended to the case of narrow bays and channels of different geometry, in the shallow-water theory framework. New analytical solutions are obtained. For a number of bottom configurations, the wave field can be found explicitly in the form of the Duhamel integral. It is described by three waves: one forced wave propagating together with the landslide and two free waves propagating in opposite directions. The cases for bays with triangular (V-shaped bay), parabolic (U-shaped bay), and rectangular cross-sections are discussed in detail. The dynamics of the offshore-propagating wave in linearly inclined bays of different cross-section are also studied asymptotically for the resonant moving landslide. Different cases of landslides of increasing and decreasing volume are considered. It is shown that even if the landslide is moving under fully resonant conditions, the amplitude of the propagating tsunami wave may still be bounded, depending on the type of the landslide.

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Acknowledgments

This research was supported by the European Union through the European Regional Development Fund. Partial support from targeted financing by the Estonian Ministry of Education and Research (grant SF0140007s11), the Estonian Science Foundation (grant 8870), the RFBR (grants 11-05-00216 and 11-02-00483), and the MK (grant 1440.2012.5) is also gratefully acknowledged. ID acknowledges the support provided by the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Laboratory of Wave Engineering, Institute of Cybernetics, Tallinn, Estonia

    Ira Didenkulova

  2. Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia

    Ira Didenkulova & Efim Pelinovsky

  3. Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod, Russia

    Efim Pelinovsky

  4. Higher School of Economics, Nizhny Novgorod, Russia

    Efim Pelinovsky

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  1. Ira Didenkulova
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Correspondence to Ira Didenkulova.

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Didenkulova, I., Pelinovsky, E. Analytical Solutions for Tsunami Waves Generated by Submarine Landslides in Narrow Bays and Channels. Pure Appl. Geophys. 170, 1661–1671 (2013). https://doi.org/10.1007/s00024-012-0510-8

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