• Journal of Korea Water Resources Association
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• v.38 no.6 s.155
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• pp.429-438
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• 2005

In this study, a couple of ordinary differential equations which can describe random waves are derived from the Boussinesq equations. Incident random waves are generated by using the TMA(TEXEL storm, MARSEN, ARSLOE) shallow-water spectrum. The governing equations are integrated with the 4-th order Runge-Kutta method. By using newly derived wave equations, nonlinear energy interaction of propagating waves in constant depth is studied. The characteristics of random waves propagate over a sinusoidally varying topography lying on a sloping beach are also investigated numerically. Transmission and reflection of random waves are considerably affected by nonlinearity.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.36 no.6
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• pp.1037-1048
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• 2016

In this study, nonlinear wave interaction in the presence of a uniform current is studied using numerical model, named CADMAS-SURF which is based on the Navier-Stokes equations coupled with Volume of Fluid for tracking free surface deformation. The original CADMAS-SURF developed for interaction of wave with structure is modified/extended to simulate nonlinear fluid dynamic motions within wave-current coexisting field. The capability of Numerical Wave-Current Tank (NWCT) in this study is validated by comparing with available existing laboratory experiments for both wave-following and wave-opposing current. The numerical results for interaction between wave and current are shown to be in good agreement with experimental data. Then, this study focused on the dynamic motions of the water velocity, surface elevation and vorticity within combined wave-current field in demonstrating complex nonlinear physical phenomena due to interaction between wave and current. In addition, NWCT is applied to simulate a more complex wave-current-structure field for wave propagating over a submerged breakwater associated with current. Detailed discussion including characteristics of velocity and vorticity fields and the relation between free surface and vorticity are given.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.197-203
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• 2008

We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

• Journal of the Society of Naval Architects of Korea
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• v.40 no.1
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• pp.20-27
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• 2003

The FPSO is moored by mooring lines to keep the position of it. The nonlinear motion analysis of the moored FPSO must be carried out in the initial design stage because sea environments affect motion of it. In this paper, the mathematical model is based on the slow motion maneuvering equations in the horizontal plane considering wave, current and wind forces. The direct integration method is employed to estimate wave loads. The current forces are calculated by using mathematical model of MMG. The turret mooring forces are quasi-statically evaluated by using the catenary equation. The coefficients of a model for wind forces are calculated from Isherwood's experimental data and the variation of wind speed is estimated by wind spectrum according to the guidelines of API-RP2A. The nonlinear motions of FPSO are simulated under external forces due to wave, current, wind including mooring forces in time domain.

• Journal of Ship and Ocean Technology
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• v.5 no.2
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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.

• Ocean Systems Engineering
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• v.3 no.2
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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.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.3
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• pp.252-261
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• 2016

A spar-type floating substructure that is being widely used for offshore wind power generation is vulnerable to resonance in the heave direction because of its small water plane area. For this reason, the stable dynamic response of this floating structure should be ensured by accurately identifying the resonance characteristics. The purpose of this study is to analyze the characteristics of the combination resonance between the excitation frequency of a regular wave and natural frequencies of the floating substructure. First, the nonlinear equations of motion with two degrees of freedom are derived by assuming that the floating substructure is a rigid body, where the heaving motion and pitching motions are coupled. Moreover, to identify the characteristics of the combination resonance, the nonlinear term in the nonlinear equations is approximated up to the second order using the Taylor series expansion. Furthermore, the validity of the approximate model is confirmed through a comparison with the results of a numerical analysis which is made by applying the commercial software ANSYS AQWA to the full model. The result indicates that the combination resonance occurs at the frequencies of ${\omega}{\pm}{\omega}_5$ and $2{\omega}_{n5}$ between the excitation frequency (${\omega}$) of a regular wave and the natural frequency of the pitching motion (${\omega}_{n5}$) of the floating substructure.

• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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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.

• Coupled systems mechanics
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• v.10 no.1
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• pp.39-60
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• 2021

The present paper is concerned with the study of nonlinear ultrasonic waves in a magneto thermo (MT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. The analytical formulation is developed based on Eringen's nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Parametric work is carried out to scrutinize the influence of the non local scaling, magneto-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter, and tube geometrical parameters have significant effects on dimensionless frequency of nano tubes. The results presented in this study can provide mechanism for the study and design of the nano devices like component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro- magneto-mechanical systems (NEMMS) that make use of the wave propagation properties of armchair single-walled carbon nanotubes embedded on polymer matrix.

• Journal of Ocean Engineering and Technology
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• v.21 no.2 s.75
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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.