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Robust Computations of Runup in Inclined U- and V-Shaped Bays

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Abstract

We present an exact analytical solution for computations of runup in constantly inclined U- and V-shaped bays. The provided solution avoids integration of indefinite double integrals in (Rybkin et al., Water Waves 3(1):267–296, 2021) and is based on a simple analytic expression for the Green’s function. We analyze wave runup in parabolic and certain V-shaped bays, for which a particularly wide class of solutions are determinable analytically and for which a robust computational algorithm could be developed. Our results are effective in the context of narrow bays, where a generalized form of the Carrier-Greenspan transformation has been developed.

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Acknowledgements

We would like to thank anonymous referees for careful reading of the manuscript and valuable comments, which have been very helpful in improving the manuscript. Alexei Rybkin acknowledges support from National Science Foundation Grant (NSF) award DMS-2009980 and DMS-1716975. Dmitry Nicolsky acknowledges support from the Geophysical Institute, University of Alaska Fairbanks. Efim Pelinovsky acknowledges support by Laboratory of Dynamical Systems and Applications NRU HSE, by the Ministry of science and higher education of the RF Grant ag. 075-15-2019-1931 and by RFBR Grant 20-05-00162. Harry Hartle was supported by the National Science Foundation Research Experience for Undergraduate program (Grant DMS-1716975).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Alaska Fairbanks, Alaska, 99775, USA

    Harrison Hartle & Alexei Rybkin

  2. Higher School of Economics, National Research University, Nizhny Novgorod, Russia

    Efim Pelinovsky

  3. Institute of Applied Physics, Nizhny Novgorod, Russia

    Efim Pelinovsky

  4. Geophysical Institute, University of Alaska Fairbanks, Alaska, 99775, USA

    Dmitry Nicolsky

  5. Saint Petersburg Electrotechnical University “LETI”, 197376, St. Petersburg, Russia

    Dmitry Nicolsky

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  1. Harrison Hartle
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  2. Alexei Rybkin
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Correspondence to Dmitry Nicolsky.

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Hartle, H., Rybkin, A., Pelinovsky, E. et al. Robust Computations of Runup in Inclined U- and V-Shaped Bays. Pure Appl. Geophys. 178, 5017–5029 (2021). https://doi.org/10.1007/s00024-021-02877-x

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