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It is shown that very steep coastal profiles can give rise to unexpectedly large wave events at the coast. We combine insight from exact solutions of a simplified mathematical model with photographs from observations at the Norwegian coast…

Atmospheric and Oceanic Physics · Physics 2020-10-05 Maria Bjørnestad , Henrik Kalisch

The numerical simulation of the nonlinear dynamics of the sea surface has shown that the collision of two groups of relatively low waves with close but noncollinear wave vectors (two or three waves in each group with a steepness of about…

Fluid Dynamics · Physics 2016-02-12 V. P. Ruban

The propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally…

The problem of tsunami wave run-up on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. We present an analysis of the run-up characteristics for various shapes of the incoming symmetrical…

Atmospheric and Oceanic Physics · Physics 2009-11-13 Ira Didenkulova , Efim Pelinovsky , Tarmo Soomere

Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been…

Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…

Chaotic Dynamics · Physics 2015-06-17 Jakob J. Metzger , Ragnar Fleischmann , Theo Geisel

The problem of the long wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. The key and novel moment here is the analysis of the runup of a certain class of asymmetric waves,…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Irina Didenkulova , Efim Pelinovsky , Tarmo Soomere , Narcisse Zahibo

Ocean rogue waves are large and suddenly appearing surface gravity waves, which may cause severe damage to ships and other maritime structures. Despite years of research, the exact origin of rogue waves is still disputed. Linear…

Atmospheric and Oceanic Physics · Physics 2015-07-30 Simon Birkholz , Carsten Brée , Ivan Veselić , Ayhan Demircan , Günter Steinmeyer

The problem of the sea wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. Key and novel moment here is the accounting of the asymmetric waves when the face slope steepness…

Pattern Formation and Solitons · Physics 2009-11-11 I. Didenkulova , N. Zahibo , A. Kurkin , B. Levin , E. Pelinovsky , T. Soomere

This paper is intended to study impact forces of breaking waves on a rigid wall based on a nonlinear potential-flow theory. This is a model problem for some technologically important design issues such as the impact of breaking waves on…

Fluid Dynamics · Physics 2014-03-13 Jian-Jun Shu

The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection…

Fluid Dynamics · Physics 2017-04-26 A. Slunyaev , M. Klein , G. F. Clauss

Recent results of numerical simulations of fully nonlinear evolutionary equations for long-crested deep-water waves are discussed, where formation of extreme waves was observed. Several examples demonstrate that three-dimensionality of the…

Atmospheric and Oceanic Physics · Physics 2011-08-19 V. P. Ruban

The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the…

Pattern Formation and Solitons · Physics 2025-08-27 Jie Zhang , Michel Benoit , Saulo Mendes

Understanding extreme ocean environments and their interaction with fixed and floating structures is critical for the design of offshore and coastal facilities. The joint effect of various ocean variables on extreme responses of offshore…

Applications · Statistics 2012-11-07 Kevin Ewans , Philip Jonathan

The processes that generate rogue waves on the sea surface remain a mystery. Despite their different natures, the nonlinear bending waves generated in a thin elastic plate share some similarities with waves on the surface of the sea. For…

Chaotic Dynamics · Physics 2025-07-17 Murukesh Muralidhar , Antoine Naert , Sébastien Aumaître

This paper describes the results from a numerical estimation of the force exerted by long surface waves on a fixed and partially immersed rectangular structure. The topic is connected with the need of making decisions on the design,…

Fluid Dynamics · Physics 2021-01-22 Oleg Gusev , Gayaz Khakimzyanov , Leonid Chubarov

The evolution of breaking waves propagating towards the shore and more specifically the run-up phase over the swash-zone for surface as well as for internal waves is considered. The study is based on a) laboratory run up experiments for…

Classical Physics · Physics 2008-02-01 Hubert Branger , Olivier Kimmoun , N. Gavrilov , Valery Liapidevskii , E. Pavlova

The runup of initial Gaussian narrow-banded and wide-banded wave fields and its statistical characteristics are investigated using direct numerical simulations, based on the nonlinear shallow water equations. The bathymetry consists of the…

Atmospheric and Oceanic Physics · Physics 2020-06-26 Ahmed Abdalazeez , Ira Didenkulova , Denys Dutykh , Céline Labart

The impact of shoaling on linear water waves is well-known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least…

Fluid Dynamics · Physics 2024-11-20 Jie Zhang , Saulo Mendes , Michel Benoit , Jérôme Kasparian

The estimation of the maximum wave sunup height is a problem of practical importance. Most of the analytical and numerical studies are limited to a constant slope plain shore and to the classical Nonlinear Shallow Water (NSW) equations.…

Classical Physics · Physics 2020-02-20 Denys Dutykh , Céline Labart , Dimitrios Mitsotakis
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