Mechanisms of Water Wave Transformation in Shear Currents

1992 ◽  
pp. 217-221
Author(s):  
Victor I. Shrira
Keyword(s):  
Water Wave ◽  
Wave Transformation

scholarly journals Novel Exact Solutions of the Extended Shallow Water Wave and the Fokas Equations

2018 ◽  
Vol 22 ◽  
pp. 01022
Author(s):  
Serbay DURAN ◽  
Berat KARAAGAC ◽  
Alaattin ESEN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Expansion Method ◽  
Travelling Wave ◽  
Wave Transformation ◽  
Partial Differential ◽  
Shallow Water Wave

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.

Improved parabolic water wave transformation model

2005 ◽  
Vol 52 (2) ◽  
pp. 139-149 ◽  
Author(s):  
U.M. Saied ◽  
I.K. Tsanis
Keyword(s):  
Water Wave ◽  
Transformation Model ◽  
Wave Transformation

scholarly journals METHOD OF ANALYSES FOR TWO-DIMENSIONAL WATER WAVE PROBLEMS

1976 ◽  
Vol 1 (15) ◽  
pp. 155 ◽  
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Akinori Yoshida
Keyword(s):  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Water Wave ◽  
Boundary Value ◽  
Wave Transformation ◽  
Two Dimensional ◽  
Simple Method ◽  
Dimensional Boundary ◽  
Horizontal Cylinders

One of the most powerful tools to analyze the boundary-value problems in water wave motion is the Green's function. However, to derive the Green's function which satisfies the imposed boundary conditions is sometimes difficult or impossible, especially in variable water depth. In this paper, a simple method of numerical analyses for two-dimensional boundary-value problems of small amplitude waves is proposed, and the wave transformation by fixed horizontal cylinders as an example of fixed boundaries, the wave transformation by and the motion of a cylinder floating on water surface as example of oscillating boundaries and the wave transformation by permeable seawall and breakwater as example of permeable boundaries are calculated and compared with experimental results.

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

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.

scholarly journals New Exact Solutions, Dynamical and Chaotic Behaviors for the Fourth-Order Nonlinear Generalized Boussinesq Water Wave Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Cheng Chen ◽  
Zuolei Wang
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Fourth Order ◽  
Water Wave ◽  
Wave Transformation ◽  
Physical Parameters ◽  
New Exact Solutions ◽  
Dynamical Behaviors ◽  
Cklund Transformation ◽  
Homogeneous Balance Method

Based on the extended homogeneous balance method, the auto-B a ¨ cklund transformation transformation is constructed and some new explicit and exact solutions are given for the fourth-order nonlinear generalized Boussinesq water wave equation. Then, the fourth-order nonlinear generalized Boussinesq water wave equation is transformed into the planer dynamical system under traveling wave transformation. We also investigate the dynamical behaviors and chaotic behaviors of the considered equation. Finally, the numerical simulations show that the change of the physical parameters will affect the dynamic behaviors of the system.

scholarly journals Numerical Modeling of Irregular Water Wave Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
K. M. Fassieh ◽  
O. Fahmy ◽  
M. A. Zaki
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Water Wave ◽  
Surf Zone ◽  
Nile Delta ◽  
Coastal Areas ◽  
Irregular Waves ◽  
Wave Transformation ◽  
Random Wave ◽  
Nile Delta Coast

Propagation of irregular water wave from deep water to a shoreline has been numerically modeled. Linear and irregular waves are considered. Model equations govern effects of shoaling, refraction, and diffraction over a varying bathymetry. The model requires the input of the incoming directional random sea at the offshore boundary. Statistical energy dissipation model is incorporated to predict realistically energy losses due to wave breaking in surf zone. Unlike most of the previous models, this model can predict wave transformation in surf zone where energy dissipation and bottom friction must be taken into consideration. The model does not have the limitation of parabolic approximation models (PAM) that are valid only in case of weak refraction. Finite difference approximations have been used to solve the governing equation. The model results are compared with experimental data for directional random wave propagation over a submerged shoal. Good agreements between the model results and experimental data are shown. Applicability of the model to real coastal areas is shown by application to coastal areas along the Nile Delta Coast, Egypt.

The coastal refraction-diffraction wave propagation model

1995 ◽  
Vol 17 (4) ◽  
pp. 6-12
Author(s):  
Nguyen Tien Dat ◽  
Dinh Van Manh ◽  
Nguyen Minh Son
Keyword(s):  
Wave Propagation ◽  
Field Data ◽  
Surf Zone ◽  
Propagation Model ◽  
Wave Transformation ◽  
Diffraction Effect ◽  
Linear Wave ◽  
Diffraction Wave ◽  
Linear Wave Propagation ◽  
Wave Propagation Model

A mathematical model on linear wave propagation toward shore is chosen and corresponding software is built. The wave transformation outside and inside the surf zone is considered including the diffraction effect. The model is tested by laboratory and field data and gave reasonables results.

PHYSICAL INTERPRETATION OF WAVE BREAKING CRITERIA

2017 ◽  
Author(s):  
Sergey Kuznetsov ◽  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Yana Saprykina ◽  
Boris Divinskiy ◽  
...  
Keyword(s):  
Nonlinear Wave ◽  
Wave Breaking ◽  
Second Harmonic ◽  
Vertical Axis ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Spectral Structure ◽  
Similarity Parameter ◽  
Nonlinear Harmonics ◽  
The Waves

On the base of experimental data it was revealed that type of wave breaking depends on wave asymmetry against the vertical axis at wave breaking point. The asymmetry of waves is defined by spectral structure of waves: by the ratio between amplitudes of first and second nonlinear harmonics and by phase shift between them. The relative position of nonlinear harmonics is defined by a stage of nonlinear wave transformation and the direction of energy transfer between the first and second harmonics. The value of amplitude of the second nonlinear harmonic in comparing with first harmonic is significantly more in waves, breaking by spilling type, than in waves breaking by plunging type. The waves, breaking by plunging type, have the crest of second harmonic shifted forward to one of the first harmonic, so the waves have "saw-tooth" shape asymmetrical to vertical axis. In the waves, breaking by spilling type, the crests of harmonic coincides and these waves are symmetric against the vertical axis. It was found that limit height of breaking waves in empirical criteria depends on type of wave breaking, spectral peak period and a relation between wave energy of main and second nonlinear wave harmonics. It also depends on surf similarity parameter defining conditions of nonlinear wave transformations above inclined bottom.

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