• Journal of Korean Society of Coastal and Ocean Engineers
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• v.23 no.5
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• pp.335-344
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• 2011

A curvilinear non-hydrostatic free surface model is developed to investigate nonlinear wave interactions in a circular channel. The proposed model solves the unsteady Navier-Stokes equations in a three-dimensional domain with a pressure correction method, which is one of fractional step methods. A hybrid staggered-grid layout in the vertical direction is implemented, which renders relatively simple resulting pressure equation as well as free surface closure. Numerical accuracy with respect to wave nonlinearity is tested against the fifth-order Stokes solution in a two-dimensional numerical wave tank. Numerical applications center on the evolution of nonlinear waves including diffraction and reflection affected by the curvature of side wall in a circular channel comparing with linear waves. Except for a highly nonlinear bichrmatic wave, the model's results are in good agreement with superimposed analytical solution that neglects nonlinear effects. Through the numerical simulation of the highly nonlinear bichramatic wave, the model shows its capability to investigate the evolution of nonlinear wave groups in a circular channel.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.2
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• pp.214-219
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• 2001

In this paper, the nonlinear behavior of ultrasonic wave in partially degraded material is considered. For this aim, FDM(finite difference method) model for the nonlinear wave equation was developed with the restriction to the 1-D longitudinal wave motion and how the partial degradation in material contributes to the detected nonlinear parameter was analyzed quantitatively. In order to verify the rightness of this simulation method, the relation between the detected nonlinear parameter and the continuous distribution of degradation obtained from simulation was compared with experiment results and the simulation and experiment results showed similar tendency. It can be known from simulation result that the degree of degradation, the range of degradation and the continuous distribution of degradation have strong correlation with the detected nonlinear parameter. As it was possible in these simulations that only special part is assumed as degraded one, the quantitative evaluation of partially degraded material may be obtained by using this method.

• Ocean Systems Engineering
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• v.4 no.2
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• pp.83-97
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• 2014

Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.

• Journal of Ocean Engineering and Technology
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• v.37 no.1
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• pp.20-30
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• 2023

Modeling a nonlinear ocean wave is one of the primary concerns in ocean engineering and naval architecture to perform an accurate numerical study of wave-structure interactions. The high-order spectral (HOS) method, which can simulate nonlinear waves accurately and efficiently, was investigated to see its capability for nonlinear wave generation. An open-source (distributed under the terms of GPLv3) project named "HOS-ocean" was used in the present study. A parametric study on the "HOS-ocean" was performed with three-hour simulations of long-crested ocean waves. The considered sea conditions ranged from sea state 3 to sea state 7. One hundred simulations with fixed computational parameters but different random seeds were conducted to obtain representative results. The influences of HOS computational parameters were investigated using spectral analysis and the distribution of wave crests. The probability distributions of the wave crest were compared with the Rayleigh (first-order), Forristall (second-order), and Huang (empirical formula) distributions. The results verified that the HOS method could simulate the nonlinearity of ocean waves. A set of HOS computational parameters was suggested for the long-crested irregular wave simulation in sea states 3 to 7.

• Journal of Ocean Engineering and Technology
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• v.31 no.6
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• pp.405-412
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• 2017

Because of the rapid development of computer technology in recent years, wave models can utilize parallel calculations for the high-resolution prediction of open sea and coastal areas with high accuracy. Parallel calculations also allow national agencies in the relevant sectors to produce marine forecasting data through massive parallel calculations. Meanwhile, the eastern coast of the Korean Peninsula has been increasingly damaged by swell-like high waves, and many researchers and scientists are continuing their efforts to anticipate and reduce the damage. In general, the short-term transformation of swell-like high waves can be reproduced relatively well in the third generation wave models, but the transformation of relatively long period waves needs to be simulated with higher accuracy in terms of the nonlinear wave interactions to gain a better understanding of the low-frequency wave generation and development mechanisms. In this study, we developed a calculation module to improve the calculation of the nonlinear energy transfer in the 3rd generation wave model and integrated it into the wave model to effectively consider the nonlinear wave interaction. First, the nonlinear energy transfer calculation module and third generation model were combined. Then, the combined model was used to reproduce the wave transformation due to the nonlinear interaction, and the performance of the developed operation module was verified.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.3
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• pp.209-218
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• 1995

Nonlinear interaction between directional wave components is theoretically analyzed in deep water. The perturbed solution for an irregular wave is derived accurate up to the third order of the wave steepness and it is shown that the wave characteristics are modulated due to the nonlinear interaction. The convergence rate of the perturbed solution depends on not only wave steepness but also wavelength ratio between wave components. The long-wave component of the perturbed solution converges rapidly. while the short-wave solution converges slowly or diverges. The short wave properties in a broad-band wave spectrum cannot accurately be obtained by the conventional wave-mode method because it fails to properly describe the modulation of short-wave frequency caused by the nonlinear interaction with much longer wave.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1998.09a
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• pp.5-11
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• 1998

Wave nonlinearity and dispersivity have mutually counteracting effects on the wave evolution process; i.e., the former makes the wave profile steeper, while the latter milder. Therefore to describe evolution of nonlinear water waves under general condition such as nonlinear random waves over arbitrary depths, both the wave nonlinearity and dispersivity must be properly taken into account in the wave modeling. (omitted)

• Journal of Navigation and Port Research
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• v.30 no.3 s.109
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• pp.181-187
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• 2006

In the wave spectrum distribution based on linear wave theory, the appearance of a giant wave whose wave height reaches to 30m has been considered next to almost impossible in a real sea However since more than 10 giant waves were observed in a recent investigation of global wave distribution which was carried out by the analysis of SAR imagines for three weeks, the existence of the giant waves is being recognized and it is considered the cause of many unknown marine disasters. The change of wave height distribution concerning a formation of wave train, nonlinear wave to wave interaction and so on were raised as the causes of the appearance of the giant waves, but the occurrence mechanism of the giant waves hasn't been cleared yet. In present study, we investigated appearance circumstances of the giant waves in real sea and its occurrence mechanism was analyzed based on linear and nonlinear wave focusing theories. Also, through a development of numerical model of the nonlinear $schr\"{o}dinger$ equation, the formations of the giant wave from progressive wave train were reproduced.

• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.1
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• pp.95-104
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• 2011

As sea state harsher in the ocean space, more large motion and wave loads occurs on ships hull by non-linear phenomena. To consider nonlinear effect on ships hull in the structural design verification, the direct calculation method with numerical approach is used rather than rule values for the reliable accuracy. In this paper, the non-linear wave loads analysis in time domain is performed by using a Rankine Panel Method together with numerical schemes. Linear calculations have been carried out based on DNV CSA-2 notation to generate the motion responses and wave loads of large ships. By short and long term analysis, the design wave amplitudes are selected for the nonlinear analysis. The maximum wave induced bending moment in hogging and sagging conditions are calculated in the nonlinear analysis. Also, the green water effect on the wave induced vertical bending moment was investigated. The results show the vertical bending moments are more influenced by green water in sagging condition than in hogging condition due to green water loading.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.977-989
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• 2000

In this paper we construct a standing solitary wave solution with prescribed total electric charge to the planer Chern-Simons gauged nonlinear Schrodinger equation with an external electromagnetic field by using a variations method.