Nonlinear wave profiles of wave–wave interaction in a finite water depth by fixed point approach

2007 ◽  
Vol 34 (3-4) ◽  
pp. 451-459 ◽  
Author(s):  
T.S. Jang ◽  
S.H. Kwon ◽  
H.S. Choi
Keyword(s):  
Fixed Point ◽  
Nonlinear Wave ◽  
Water Depth ◽  
Wave Interaction ◽  
Fixed Point Approach ◽  
Finite Water Depth ◽  
Wave Profiles

Numerical Simulation of 5th-Order Stokes Wave in Finite Water Depth Based on Momentum Source Method

2021 ◽  
Author(s):  
Wenjie Wang ◽  
Zhiliang Gao
Keyword(s):  
Numerical Simulation ◽  
Water Depth ◽  
Present Method ◽  
Wave Interaction ◽  
Wave Generation ◽  
Stokes Wave ◽  
Wave Loads ◽  
Large Wave ◽  
Wave Flume ◽  
Finite Water Depth

Abstract For numerical simulation of structure-wave interaction, the wave generation with high accuracy is prime to analyze the wave loads and motions of the structure. Based on the fifth-order Stokes theory, a two-dimensional viscous wave flume, which was modeled using the commercial CFD solver ANSYS-FLUENT, was applied to the generation and propagation of regular waves in finite water depth. With the user-defined function provided by the solver, the momentum source term and boundary condition, which are used for the wave generation and dissipation, were developed to ensure the accuracy of wave simulation with large steepness. In addition, the wave flume was separated into two regions, which are governed by the laminar model and turbulent model, respectively. The separation of laminar and turbulent regions can alleviate the side effect of turbulence on the accuracy of wave generation. In order to validate the present method, the regular wave propagating with different steepness in finite water depth were simulated. The numerical results were in good agreement with the theoretical ones. The study showed that the present method was effective for the simulation of Stokes wave in finite water depth, especially effective to improve the numerical accuracy in case of large wave steepness.

A nonlinear wave profile correction of the diffraction of a wave by a long breakwater: Fixed point approach

2007 ◽  
Vol 34 (3-4) ◽  
pp. 500-509 ◽  
Author(s):  
T.S. Jang ◽  
S.H. Kwon ◽  
Takeshi Kinoshita ◽  
B.J. Kim
Keyword(s):  
Fixed Point ◽  
Nonlinear Wave ◽  
Wave Profile ◽  
Fixed Point Approach ◽  
Profile Correction

scholarly journals HIGH ORDER NONLINEAR WAVE INTERACTIONS FROM DEEP TO FINITE WATER DEPTH WITH BOTTOM TOPOGRAPHY CHANGE

2020 ◽  
pp. 24
Author(s):  
Zuorui Lyu ◽  
Hiroaki Kashima ◽  
Nobuhito Mori
Keyword(s):  
Nonlinear Wave ◽  
Water Depth ◽  
Deep Water ◽  
Modulational Instability ◽  
High Order ◽  
Long Distance ◽  
Freak Wave ◽  
Wave Evolution ◽  
Finite Water Depth ◽  
Skewness And Kurtosis

In recent years, freak wave/rouge wave has become an important problem in science and engineering. Modulational instability is considered to be an important factor leading to freak wave in the wave evolution of deep water, and Janssen (2003) defined Benjamin-Feir index (BFI) to reflect it. Mori and Janssen (2006) gave the occurrence probability of freak waves based on a weakly non-Gaussian theory, and distribution of wave height is determined by skewness and kurtosis of surface elevation to a considerable extent in deep water. According to observational record, freak wave has not only been found in deep water in the ocean, but also been observed in shallow water and coastal areas. In the process of water wave entering continental shelf, water depth is changing with mild slope after a long distance propagation. This study focus on investigating how water depth affect skewness and kurtosis in the high order nonlinear wave evolution from deep water to finite water depth in two-dimension.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/a8LiJvXWRrw

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

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