• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.391-398
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• 2024

This article explains how solitons propagate when there is a detuning factor involved. The explanation is based on the nonlinear complex Ginzburg-Landau equation, and we first consider this equation before systematically deriving its solutions using Jacobian elliptic functions. We illustrate that one specific ellipticity modulus is on the verge of occurring. The findings from this study can contribute to the understanding of previous research on the Ginzburg-Landau equation. Additionally, we utilize Jacobi's elliptic functions to define specific solutions, especially when the ellipticity modulus approaches either unity or zero. These solutions correspond to particular periodic wave solitons, which have been previously discussed in the literature.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.611-624
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• 2010

A Numerical scheme based on collocation method using quartic B-spline functions is designed for the numerical solution of one-dimensional modified equal width wave (MEW) wave equation. Using Von-Neumann approach the scheme is shown to be unconditionally stable. Performance of the method is validated through test problems including single wave, interaction of two waves and use of Maxwellian initial condition. Using error norms $L_2$ and $L_{\infty}$ and conservative properties of mass, momentum and energy, accuracy and efficiency of the suggested method is established through comparison with the existing numerical techniques.

• Journal of Ship and Ocean Technology
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• 제5권2호
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• pp.50-61
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• 2001

In this paper, nonlinear interactions between water waves and a horizontally submerged circular cylinder are numerically simulated. In this case, the nonlinear interactions between them generated a wave breaking phenomenon. The wave breaking phenomenon plays an important role in the wave farce. Negative drifting forces are raised at shallow submerged cylinders under waves because of the wave breaking phenomenon. For the numerical simulation, a finite difference method based on the unsteady incompressible Navier-Stokes equations and the continuity equation is adopted in the rectangular grid system. The free surface is simulated with a computational simulation method of two-layer flow by using marker density. The results are compared with some existing computational and experimental results.

• 한국해양공학회지
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• 제19권4호
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• pp.1-8
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• 2005

A nonlinear time-domain strip theory for vertical wave loads and ship responses is to be investigated. The hydrodynamic memory effect is approximated by a higher order differential equation without convolution. The ship is modeled as a non-uniform Timoshenko beam. Numerical calculations are presented for the S175 Containership translating with the forward speed in regular waves. The approach described in this paper can be used in evaluating ship motions and wave loads in extreme wave conditions and validating nonlinear phenomena in ship design.

• Ocean Systems Engineering
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• 제3권2호
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• pp.149-165
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• 2013

Tension leg platforms (TLP's) are highly nonlinear due to large structural displacements and fluid motion-structure interaction. Therefore, the nonlinear dynamic response of TLP's under hydrodynamic wave loading is necessary to determine their deformations and dynamic characteristics. In this paper, a numerical study using modified Morison Equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between all degrees of freedom on the dynamic behavior of a TLP. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark's beta integration scheme. The effect of wave characteristics was considered.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2007년도 추계 학술대회논문집
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• pp.134-140
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• 2007

Nonlinear parabolized stability equations for compressible flow in general curvilinear coordinate system are derived to deal with a broad range of transition prediction problems on complex geometry. A highly accurate finite difference PSE code has been developed using an implicit marching procedure. Blasius flow is tested. The results of the present computation show good agreement with DNS data. Nonlinear interaction can make the T-S fundamental wave more unstable and the onset of its amplitude decay is shifted downstream relative to linear case. For nonlinear calculations, rather small difference in initial amplitude can produce large change during nonlinear region. Compressible secondary instability at Mach number 1.6 is also simulated and showed that 1.1% initial amplitude for primary mode is enough to trigger the secondary growth.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 1998년도 추계학술대회논문집:21세기에 대비한 지능형 통합항만관리
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• pp.189-199
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• 1998

Wave-induced current model is developed in our study and this model is composed with wave transform model and current model. Two types of wave model are used in our study, one is Copeland(1985) type which is applied in the offshore region and the other is Watanabe and Maruyama(1984) type which is applied in the surf zone. The depth-integrated and time-averaged governing equation of an unsteady nonlinear form is used in the wave induced current model. Lateral mising, radiation stresses, surface and bottom stresses are considered in our current model. Copeland's(1985) relult is used to calculate radiation stress and Berkmeir & Darlymple's(1976) is used as a surface friction formula. Numerical solutions are obtained by Leendertse scheme and compared with Noda's(1974) experimental results for the uniform slope coastal region test and Nishimura & Maruyama's(1985) experimental relults and numerical simulation results for the detached breakwater test. The results from our wave model show good agreement with the others and also show nonlinear effects around the detached breakwater. Wave induced current model is developed in this study and this model shows nonlinear effects around the detached breakwater and can be applied in the surf zone and also consider the friction stresses.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 12th Asian Congress of Fluid Mechanics
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• pp.33.1-33.1
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• 2008

• 한국해양공학회지
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• 제21권2호
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• pp.12-21
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• 2007

As the economy grows and the population increases, we need to develop our coastal area and make use of it for various purposes. Specifically, investigation of the wave interactions on and around the vertical cylinders is very important in the design of the offshore or coastal structures. The nonlinear potential analysis developed so far, although very useful, has been found to be limited in application, as strong nonlinear waves generated by the interference between multilayered cylinders and wave impact forces by breaking waves can hardly be estimated. In this study, using a 3-Dimensional volume tracking method VOF(Volume of Fluid), based on Namer-Stokes equations, was developed to simulate highly nonlinear effects, such as breaking waves at the interface or complicated interference waves among structures. A numerical method for nonlinear interaction wave and vertical cylinders is newly proposed. The wave forces and wave transformations computed by the newly proposed numerical simulation method were compared to the other researcher's experimental results, and the results agree well. Based on the validation of this study, this numerical method is applied to the two vertical cylinders to discuss their nonlinear wave forces and wave transformations, according to the variations of separate distance of vertical cylinders.

• 한국해안·해양공학회논문집
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• 제33권6호
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• pp.257-264
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• 2021

본 연구는 완전비선형 Boussinesq 방정식 모델인 FUNWAVE-TVD 모델을 이용하여 비선형 불규칙파에 의한 해안구조물의 월파량을 산정할 수 있는 수치모형을 수립한 것이다. 여기서는 EurOtop(2018)의 월파량 산정 식 및 Goda(2009)의 경험식을 코딩하여 FUNWAVE-TVD 모델의 서브루틴으로 추가하고 수치모형을 수립하였다. 모형의 검증은 직립구조물에 대한 비선형 불규칙파의 월파량을 수치계산하고 EurOtop(2018)에 제시된 실험 결과와 비교하여 수행하였다. EurOtop 식에 의한 수치계산 결과는 비쇄파 조건의 경우 모든 상대여유고(Rc/Hmo) 구간에서 실험결과와 매우 잘 일치하였으며, 경험식에 의한 수치계산 결과는 R_c/H_mo < 0.8 구간에서는 실험 결과보다 과소평가 되었고 R_c/H_mo < 0.8의 구간에서는 실험 결과보다 과대평가 되었다. 쇄파조건의 경우 본 모형의 결과는 R_c/H_mo ≤ 1.35의 exponential curve나 R_c/H_mo > 1.35의 power curve 구간 모두에서 실험 결과를 잘 재현하였다. 따라서 본 수치모형은 직립구조형식의 호안구조물에서 비선형 불규칙파에 의한 월파량을 정도 높게 모의할 수 있음을 확인하였다.