BOUNDARY TECHNIQUE FOR CALCULATION OF WAVE TRANSFORMATION ON STEP TOPOGRAPHY IN SHALLOW WATER

In this study, a Sine-Gordon expansion method for obtaining novel exact solutions of extended shallow water wave equation and Fokas equation is presented. All of the equations which are under consideration consist of three or four variable. In this method, first of all, partial differential equations are reduced to ordinary differential equations by the help of variable change called as travelling wave transformation, then Sine Gordon expansion method allows us to obtain new exact solutions defined as in terms of hyperbolic trig functions of considered equations. The newly obtained results showed that the method is successful and applicable and can be extended to a wide class of nonlinear partial differential equations.

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WAVE DECAYING DUE TO BREAKING

Coastal Engineering Proceedings ◽

10.9753/icce.v10.15 ◽

1966 ◽

Vol 1 (10) ◽

pp. 15 ◽

Cited By ~ 4

Author(s):

Makoto Nakamura ◽

Hidehiko Shiraishi ◽

Yasuo Sasaki

Keyword(s):

Shallow Water ◽

Deep Sea ◽

River Mouth ◽

Beach Erosion ◽

Breaking Point ◽

Wave Transformation ◽

Effective Measure ◽

Planning And Design ◽

Sea Bottom ◽

Sea Area

In the planning and design of coastal engineering works for the control of beach characteristics, a proper and effective measure against wave must be the most important problem to be solved. When the wave generated on the open sea approaches the shallow sea area, it will be transformed under the influence of sea bottom. For the construction works of coastal structures on a shoreline or in shallow water, the estimation of the rate of wave transformation is needed. In this concern, many reports were already published by the researchers,i. e, R.L.Wiegel, M.A.Mason,H.W. Iversen and T.Kishi. Moreover, the so-called Breaker Index which shows the breaking conditions has been obtained by the Beach Erosion Bord (U.S.A.), based on the data of field observations. Furthermore, these characteristics were investigated theoretically and experimentally by H.W. Iversen, Hamada, Sato and Kishi. Though these results show the wave transformation from the deep sea to a breaking point, there are few reports dealing with the wave transformation in the process of breaking and after a breaker zone. In the execution of coastal works projected in Ministry of Agriculture and Forestry such as shore reclamation works, coastal defence works and river mouth improvement, the wave inshore from a breaker zone often should be taken into consideration. In the past design of coastal structure, the wave acting on structures in the shallow water is calculated from the deep sea wave usually by using very rough estimation that wave height is reduced by about 30 per cent after a single breaking and wave period by about 10 per cent. Consequently, in order to analyze the wave decaying due to breaking, this paper treated with the wave transformation in the vicinity of a breaking point.

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Plenty of wave solutions to the ill-posed Boussinesq dynamic wave equation under shallow water beneath gravity

AIMS Mathematics ◽

10.3934/math.2022005 ◽

2021 ◽

Vol 7 (1) ◽

pp. 63-90

Author(s):

Mostafa M. A. Khater ◽

◽

S. H. Alfalqi ◽

J. F. Alzaidi ◽

Samir A. Salama ◽

...

Keyword(s):

Solitary Wave ◽

Shallow Water ◽

Evolution Equations ◽

Nonlinear Evolution Equations ◽

Wave Transformation ◽

Computational Techniques ◽

Solitary Wave Solutions ◽

Wave Solutions ◽

Ill Posed ◽

Dynamic Wave

<abstract><p>This paper applies two computational techniques for constructing novel solitary wave solutions of the ill-posed Boussinesq dynamic wave (IPB) equation. Jacques Hadamard has formulated this model for studying the dynamic behavior of waves in shallow water under gravity. Extended simple equation (ESE) method and novel Riccati expansion (NRE) method have been applied to the investigated model's converted nonlinear ordinary differential equation through the wave transformation. As a result of this research, many solitary wave solutions have been obtained and represented in different figures in two-dimensional, three-dimensional, and density plots. The explanation of the methods used shows their dynamics and effectiveness in dealing with certain nonlinear evolution equations.</p></abstract>

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Dynamic interaction of behaviors of time-fractional shallow water wave equation system

Modern Physics Letters B ◽

10.1142/s021798492150353x ◽

2021 ◽

pp. 2150353

Author(s):

Serbay Duran

Keyword(s):

Wave Equation ◽

Shallow Water ◽

Traveling Wave ◽

Water Wave ◽

Traveling Wave Solutions ◽

Equation System ◽

Wave Transformation ◽

Trigonometric Functions ◽

Shallow Water Wave ◽

Wave Solutions

In this study, the traveling wave solutions for the time-fractional shallow water wave equation system, whose physical application is defined as the dynamics of water bodies in the ocean or seas, are investigated by [Formula: see text]-expansion method. The nonlinear fractional partial differential equation is transformed to the non-fractional ordinary differential equation with the use of a special wave transformation. In this special wave transformation, we consider the conformable fractional derivative operator to which the chain rule is applied. We obtain complex hyperbolic and complex trigonometric functions for the time-fractional shallow water wave equation system with the help of this technique. New traveling wave solutions are obtained for the special values given to the parameters in these complex hyperbolic and complex trigonometric functions, and the behavior of these solutions is examined with the help of 3D and 2D graphics.

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RAPID CALCULATION OF NONLINEAR WAVE-WAVE INTERACTIONS

Coastal Engineering Proceedings ◽

10.9753/icce.v32.waves.36 ◽

2011 ◽

Vol 1 (32) ◽

pp. 36 ◽

Cited By ~ 1

Author(s):

Lihwa Lin ◽

Zeki Demirbilek ◽

Jinhai Zheng ◽

Hajime Mase

Keyword(s):

Energy Transfer ◽

Shallow Water ◽

Nonlinear Wave ◽

Ocean Waves ◽

Wave Transformation ◽

Calculation Algorithm ◽

Wave Interactions ◽

Nonlinear Energy Transfer ◽

Rapid Calculation ◽

Nonlinear Energy

This paper presents an efficient numerical algorithm for the nonlinear wave-wave interactions that can be important in the evolution of coastal waves. Indeed, ocean waves truly interact with each others. However, because ocean waves can also interact with the atmosphere such as under variable wind and pressure fields, and waves will deform from deep to shallow water, it is generally difficult to differentiate the actual amount of the nonlinear energy transfer among spectral waves mixed with the atmospheric input and wave breaking. The classical derivation of the nonlinear wave energy transfer has involved tedious numerical calculation that appears impractical to the engineering application. The present study proposed a theoretically based formulation to efficiently calculate nonlinear wave-wave interactions in the spectral wave transformation equation. It is approved to perform well in both idealized and real application examples. This rapid calculation algorithm indicates the nonlinear energy transfer is more significant in the intermediate depth than in deep and shallow water conditions.

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ESTIMATION OF BOUND AND RELEASED INFRAGRAVITY WAVES BASED ON WAVE OBSERVATION AND NUMERICAL SIMULATION IN SHALLOW WATER

Coastal Engineering Proceedings ◽

10.9753/icce.v36.currents.37 ◽

2018 ◽

pp. 37

Author(s):

Katsuya Hirayama ◽

Hiroaki Kashima ◽

Yoshiyuki Uno

Keyword(s):

Numerical Simulation ◽

Shallow Water ◽

Wave Spectrum ◽

Short Wave ◽

Wave Transformation ◽

Boussinesq Model ◽

Release Process ◽

Infragravity Waves ◽

Standard Spectrum ◽

Wave Observation

It is mentioned that observed infragravity waves consist of bound waves propagating with short-wave groups, released waves due to reduction of short crest waves and free waves existing in a field. Though it is difficult to distinguish among them, a standard spectrum for infragravity waves is defined by using a relation to a wind wave spectrum. In this study, a comprehensive definition of standard spectrum is newly proposed to estimate infragravity wave heights with the relation between the ratio of wave height and the ursell number of observed wave property, represented by selected data of wave observation in shallow water. Moreover, the release process of bound waves at a harbor entrance is reproduced in numerical simulation using a Boussinesq model for short-wave transformation. These results are verified by comparison to infragravity waves observed at outside/inside of a harbor for a month.

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GENERATION OF EXTREME TRANSIENT WAVES IN EXPERIMENTAL MODELS

Coastal Engineering Proceedings ◽

10.9753/icce.v36.waves.51 ◽

2018 ◽

pp. 51

Author(s):

Huichen Zhang ◽

Markus BrÃ¼hl

Keyword(s):

Shallow Water ◽

Nonlinear Wave ◽

Wave Generation ◽

Experimental Models ◽

Scale Model ◽

Wave Transformation ◽

Wave Analysis ◽

Transient Waves ◽

Wave Interactions ◽

Wave Flume

The transfer of natural waves and sea states into small- and large-scale model teste contributes to the proper design of offshore and coastal structure. Such shallow-water ocean surface waves are highly nonlinear and subject to wave transformation and nonlinear wave-wave interactions. However, the standard methods of wave generation according to conventional wave theories and wave analysis methods are limited to simple regular waves, simple sea states and low-order wave generation without considering the nonlinear wave-wave interactions. The research project Generation of Extreme Transient Waves in Experimental Models (ExTraWaG) aims to accurately generate target transient wave profile at a pre-defined position in the wave flume (transfer point) under shallow water conditions. For this purpose, the KdV-based nonlinear Fourier transform is introduced as a continuative wave analysis method and is applied to investigate the nonlinear spectral character of experimental wave data. Furthermore, the method is applied to generate transient nonlinear waves as specific locations in the wave flume, considering the nonlinear transformation and interactions of the propagating waves.

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