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Discussion papers
https://doi.org/10.5194/nhess-2019-176
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/nhess-2019-176
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 06 Jun 2019

Research article | 06 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).

Probabilistic characteristics of narrow-band long wave run-up onshore

Sergey Gurbatov1 and Efim Pelinovsky2,3 Sergey Gurbatov and Efim Pelinovsky
  • 1National Research University – Lobachevsky State University, Nizhny Novgorod, Russia
  • 2National Research University – Higher School of Economics, Moscow, Russia
  • 3Institute of Applied Physics, Nizhny Novgorod, Russia

Abstract. The run-up of random long wave ensemble (swell, storm surge and tsunami) on the constant-slope beach is studied in the framework of the nonlinear shallow-water theory in the approximation of non-breaking waves. If the incident wave approaches the shore from deepest water, runup characteristics can be found in two stages: at the first stage, linear equations are solved and the wave characteristics at the fixed (undisturbed) shoreline are found, and, at the second stage, the nonlinear dynamics of the moving shoreline is studied by means of the Riemann (nonlinear) transformation of linear solutions. In the paper, detail results are obtained for quasi-harmonic (narrow-band) waves with random amplitude and phase. It is shown that the probabilistic characteristics of the runup extremes can be found from the linear theory, while the same ones of the moving shoreline – from the nonlinear theory. The role of wave breaking due to large-amplitude outliers is discussed, so that it becomes necessary to consider wave ensembles with non-Gaussian statistics within the framework of the analytical theory of non-breaking waves. The basic formulas for calculating the probabilistic characteristics of the moving shoreline and its velocity through the incident wave characteristics are given. They can be used for estimates of the flooding zone characteristics in marine natural hazards.

Sergey Gurbatov and Efim Pelinovsky
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Sergey Gurbatov and Efim Pelinovsky
Sergey Gurbatov and Efim Pelinovsky
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Short summary
Very often hazardous sea waves approach to the coast having irregular structure. They should be characterized by the statistical characteristics. They are found here within analytical theory of shallow-water wave runup on a beach without breaking. Obtained distribution functions can be used for estimates of the flooding zone characteristics in marine natural hazards.
Very often hazardous sea waves approach to the coast having irregular structure. They should be...
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