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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/nhess-2019-182
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/nhess-2019-182
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 20 Jun 2019

Submitted as: research article | 20 Jun 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Natural Hazards and Earth System Sciences (NHESS).

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

Ahmed A. Abdalazeez1, Ira Didenkulova1,2, and Denys Dutykh3 Ahmed A. Abdalazeez et al.
  • 1Department of Marine Systems, Tallinn University of Technology, Akadeemia tee 15A, Tallinn 12618, Estonia
  • 2Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Minin str. 24, Nizhny Novgorod 603950, Russia
  • 3Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, Chambéry, 73000, France

Abstract. The estimate of individual wave run-up is especially important for tsunami warning and risk assessment as it allows to evaluate the inundation area. Here as a model of tsunami we use the long single wave of positive polarity. The period of such wave is rather long which makes it different from the famous Korteweg–de Vries soliton. This wave is nonlinearly deformed during its propagation in the ocean which results in a steep wave front formation. Situations, when waves approach the coast with a steep front are often observed during large tsunamis, e.g. 2004 Indian Ocean and 2011 Tohoku tsunamis. Here we study the nonlinear deformation and run-up of long single waves of positive polarity in the conjoined water basin, which consists of the constant depth section and a plane beach. The work is performed numerically and analytically in the framework of the nonlinear shallow water theory. Analytically, wave propagation along the constant depth section and its run-up on a beach are considered independently without taking into account wave reflection from the toe of the bottom slope. The propagation along the bottom of constant depth is described by Riemann wave, while the wave run-up on a plane beach is calculated using rigorous analytical solutions of the nonlinear shallow water theory following the Carrier–Greenspan approach. Numerically, we use the finite volume method with the second order UNO2 reconstruction in space and the third order Runge–Kutta scheme with locally adaptive time steps. During wave propagation along the constant depth section, the wave becomes asymmetric with a steep wave front. Shown, that the maximum run-up height depends on the front steepness of the incoming wave approaching the toe of the bottom slope. The corresponding formula for maximum run-up height which takes into account the wave front steepness is proposed.

Ahmed A. Abdalazeez et al.
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Ahmed A. Abdalazeez et al.
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Short summary
This work is based on the authors' idea that asymmetry of the tsunami wave gained during its propagation in the ocean should also influence its run-up height on the slope. This was previously analytically shown by the authors for sinusoidal waves. In the given manuscript, this idea is elaborated for single waves using both semi-analytical and numerical methods. The corresponding formula for maximum run-up height which takes into account the wave front steepness is proposed.
This work is based on the authors' idea that asymmetry of the tsunami wave gained during its...
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