Run-Up Simulation of Impulse-Generated Solitary Waves

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

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On the numerical simulation of the nonbreaking solitary waves run up on sloping beaches

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2015.09.001 ◽

2015 ◽

Vol 70 (9) ◽

pp. 2270-2281 ◽

Cited By ~ 4

Author(s):

Asghar Farhadi ◽

Homayoun Emdad ◽

Ebrahim Goshtasbi Rad

Keyword(s):

Numerical Simulation ◽

Solitary Waves ◽

Run Up

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Dispersive mudslide-induced tsunamis

Nonlinear Processes in Geophysics ◽

10.5194/npg-5-127-1998 ◽

1998 ◽

Vol 5 (3) ◽

pp. 127-136 ◽

Cited By ~ 1

Author(s):

A. Rubino ◽

S. Pierini ◽

J. O. Backhaus

Keyword(s):

Solitary Waves ◽

Intermediate Phase ◽

Water Model ◽

Tsunami Propagation ◽

Tsunami Waves ◽

Open Sea ◽

Petviashvili Equation ◽

Wave Forms ◽

Generation Region ◽

Run Up

Abstract. A nonlinear nested model for mudslide-induced tsunamis is proposed in which three phases of the life of the wave, i.e. the generation, far-field propagation and costal run-up are described by means of different mathematical models, that are coupled through appropriate matching procedures. The generation and run-up dynamics are simulated through a nonlinear shallow-water model with movable lateral boundaries: in the generation region two active layers are present, the lower one describing the slide descending on a sloping topography. For the intermediate phase, representing wave propagation far from the generation region, the hydrostatic assumption is not assumed as appropriate in general and, therefore, a nonlinear model allowing for weak phase dispersion, namely a Kadomtsev-Petviashvili equation, is used. This choice is made in order to assess the relevance of dispersive features such as solitary waves and dispersive tails. It is shown that in some realistic circumstances dispersive mudslide-induced tsunami waves can be produced over relatively short, distances. In such cases the use of a hydrostatic model throughout the whole tsunami history turns out to give erroneous results. In particular, when solitary waves are generated during the tsunami propagation in the open sea, the resulting run-up process yields peculiar wave forms leading to amplified coastal inundations with respect to a mere hydrostatic context.

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LARGE SCALE EXPERIMENTS ON EVOLUTION AND RUN-UP OF BREAKING SOLITARY WAVES

Journal of Earthquake and Tsunami ◽

10.1142/s1793431107000158 ◽

2007 ◽

Vol 01 (03) ◽

pp. 257-272 ◽

Cited By ~ 3

Author(s):

KAO-SHU HWANG ◽

YU-HSUAN CHANG ◽

HWUNG-HWENG HWUNG ◽

YI-SYUAN LI

Keyword(s):

Solitary Wave ◽

Wave Height ◽

Solitary Waves ◽

Water Depth ◽

Large Scale ◽

Scale Effects ◽

Wave Heights ◽

Run Up ◽

Hydraulics Laboratory ◽

The Waves

The evolution and run-up of breaking solitary waves on plane beaches are investigated in this paper. A series of large-scale experiments were conducted in the SUPER TANK of Tainan Hydraulics Laboratory with three plane beaches of slope 0.05, 0.025 and 0.017 (1:20, 1:40 and 1:60). Solitary waves of which relative wave heights, H/h0, ranged from 0.03 to 0.31 were generated by two types of wave-board displacement trajectory: the ramp-trajectory and the solitary-wave trajectory proposed by Goring (1979). Experimental results show that under the same relative wave height, the waveforms produced by the two generation procedures becomes noticeably different as the waves propagate prior to the breaking point. Meanwhile, under the same relative wave height, the larger the constant water depth is, the larger the dimensionless run-up heights would be. Scale effects associated with the breaking process are discussed.

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The run-up of N -waves on sloping beaches

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0050 ◽

1994 ◽

Vol 445 (1923) ◽

pp. 99-112 ◽

Cited By ~ 179

Keyword(s):

Solitary Waves ◽

Wave Model ◽

Propagation Distance ◽

Order Theory ◽

New Paradigm ◽

Asymptotic Results ◽

Tsunami Waves ◽

First Order Theory ◽

Run Up ◽

Tsunami Run Up

Anecdotal reports of tsunamis climbing up coastlines have often described the shoreline receding significantly before the tsunami waves run-up on the beach. These waves are caused by tsunamigenic earthquakes close to the shoreline, when the generated wave does not have sufficient propagation distance to evolve into leading-elevation waves or a series of solitary waves. Yet all previous run-up investigations have modelled periodic waves or solitary waves which initially only run-up on the beach. In our studies of these initially receding shorelines, we have found a class of N -shaped waves with very interesting and counterintuitive behaviour which may lead to a new paradigm for the studies of tsunami run-up. We will use a first-order theory and we will derive asymptotic results for the maximum run-up within the validity of the theory for different types of N -waves. We have observed that leading depression N -waves run-up higher than leading elevation N -waves, suggesting that perhaps the solitary wave model may not be adequate for predicting an upper limit for the run-up of near-shore generated tsunamis.

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Run-up of non-breaking double solitary waves with equal wave heights on a plane beach

Journal of Hydrodynamics ◽

10.1016/s1001-6058(14)60103-7 ◽

2014 ◽

Vol 26 (6) ◽

pp. 939-950 ◽

Cited By ~ 4

Author(s):

Jie Dong ◽

Ben-long Wang ◽

Hua Liu

Keyword(s):

Solitary Waves ◽

Wave Heights ◽

Run Up

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CFD Analysis of Water Solitary Wave Reflection

The Journal of Engineering Research [TJER] ◽

10.24200/tjer.vol8iss2pp10-18 ◽

2011 ◽

Vol 8 (2) ◽

pp. 10 ◽

Cited By ~ 1

Author(s):

K. Smida ◽

H. Lamloumi ◽

K. Maalel ◽

Z. Hafsia

Keyword(s):

Solitary Wave ◽

Solitary Waves ◽

Stokes Equations ◽

Vertical Wall ◽

Wave Generation ◽

Navier Stokes ◽

Computational Domain ◽

Collision Process ◽

Linear Waves ◽

Run Up

A new numerical wave generation method is used to investigate the head-on collision of two solitary waves. The reflection at vertical wall of a solitary wave is also presented. The originality of this model, based on the Navier-Stokes equations, is the specification of an internal inlet velocity, defined as a source line within the computational domain for the generation of these non linear waves. This model was successfully implemented in the PHOENICS (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series) code. The collision of two counter-propagating solitary waves is similar to the interaction of a soliton with a vertical wall. This wave generation method allows the saving of considerable time for this collision process since the counter-propagating wave is generated directly without reflection at vertical wall. For the collision of two solitary waves, numerical results show that the run-up phenomenon can be well explained, the solution of the maximum wave run-up is almost equal to experimental measurement. The simulated wave profiles during the collision are in good agreement with experimental results. For the reflection at vertical wall, the spatial profiles of the wave at fixed instants show that this problem is equivalent to the collision process.

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BREAKING AND WASH UP OF SOLITARY WAVES ON A COMPOSITE BEACH

Coastal Engineering Proceedings ◽

10.9753/icce.v36v.waves.29 ◽

2020 ◽

pp. 29

Author(s):

Hajo von Hafen ◽

Jacob Stolle ◽

Nils Goseberg ◽

Ioan Nistor

Keyword(s):

Solitary Waves ◽

Horizontal Plane ◽

Large Scale ◽

Propagation Path ◽

Rock Falls ◽

Damage Potential ◽

Large Wave ◽

Beach Slope ◽

Wave Flume ◽

Run Up

Hazardous events, such as landslides, rock slides, rock falls or avalanches often generate extreme, impulsive waves when entering water bodies (Fuchs & Hager, 2015). These waves are approximated by solitary waves and researchers investigate their damage potential when inundating built environment. Deepening the understanding of solitary waves running up a uniform beach slope and propagating over a subsequent horizontal plane can help to reduce and mitigate damage and the number of casualties caused by such a hazardous event. So far, few authors addressed this specific setting near-shore (Fuchs & Hager, 2015; Zelt & Raichlen, 1991). In this study, large scale solitary waves propagate about 200 m in in the Large-Wave Flume (GWK, 307 m 5 m 7 m) at the Coastal Research Center in Hannover, Germany then they run up a beach slope and subsequently break, generating a bore which advances onto a subsequent, initially dry, horizontal surface. Unlike previous studies, the generated solitary waves broke close to the edge between the beach slope and the horizontal plane section. The overall aim of this study is to investigate the characteristics of the broken waves' dynamics. In addition, their surge profile and front celerity are compared to those of the non-breaking solitary waves. Subsequently, the differences between the velocity regimes along the bore propagation path are presented and linked to the fundamental physical processes behind.

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