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The run-up of nonlinearly deformed sea waves on the coast of a bay with a parabolic cross-section

  • Physics of Earth, Atmosphere, and Hydrosphere
  • Published:
Moscow University Physics Bulletin Aims and scope

Abstract

The run-up of long waves on the coast of a bay with a parabolic cross-section, where the region of constant depth along the principal axis of the bay is connected with the linearly inclined segment, is considered. The study is carried out analytically in the framework of the nonlinear shallow-water theory under the approximation that the height of the initial wave is small compared to the basin depth, and the reflection from the inflection point of the bottom is negligibly small. Three types of incident waves, viz., a sinusoidal wave and solitary waves of positive and negative polarities, are considered in detail. It is shown that a sinusoidal wave undergoes nonlinear deformation at a segment of constant depth faster than solitary waves of positive and negative polarities. Solitary waves of negative polarity steepen somewhat faster than solitary waves of positive polarity. Waves of positive polarity steepen at wave front, while waves of negative polarity steepen at wave rear. These differences in steepness may become crucial at the wave run-up stage, since the wave run-up height on the coast of a bay with a parabolic cross-section is directly proportional to the steepness of a wave that arrives at the slope and can lead to the anomalous run-up of waves on the coast.

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Authors and Affiliations

  1. Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, 603950, Russia

    O. I. Didenkulov, I. I. Didenkulova & E. N. Pelinovsky

  2. Marine Systems Institute, Tallinn University of Technology, Tallinn, 12618, Estonia

    I. I. Didenkulova

  3. Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, 603950, Russia

    E. N. Pelinovsky

Authors
  1. O. I. Didenkulov
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  2. I. I. Didenkulova
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  3. E. N. Pelinovsky
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Corresponding author

Correspondence to O. I. Didenkulov.

Additional information

Original Russian Text © O.I. Didenkulov, I.I. Didenkulova, E.N. Pelinovsky, 2016, published in Vestnik Moskovskogo Universiteta, Seriya 3: Fizika, Astronomiya, 2016, No. 3, pp. 86–91.

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Didenkulov, O.I., Didenkulova, I.I. & Pelinovsky, E.N. The run-up of nonlinearly deformed sea waves on the coast of a bay with a parabolic cross-section. Moscow Univ. Phys. 71, 323–328 (2016). https://doi.org/10.3103/S0027134916030048

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  • DOI: https://doi.org/10.3103/S0027134916030048

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