• 대한기계학회논문집A
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• 제25권2호
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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.

• 한국해양공학회지
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• 제37권1호
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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.

• 한국해안·해양공학회논문집
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• 제29권4호
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• pp.169-179
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• 2017

본 연구에서는 선형 및 비선형파의 안정적이고 정확한 조파를 위해 이완법을 이용한 조파기법을 비정수압 수치모형인 SWASH 모형에 적용하였다. 이완법을 이용한 조파기법을 검증하기 위해 선형파와 비선형파인 경우에 대해 수치실험을 수행하였고 해석해와 비교하였다. 그 결과 Stokes 파 영역으로부터 cnoidal 파 영역에 이르는 모든 경우의 입사파랑이 성공적으로 생성되고 전파되었다. 또한 파고와 파형이 해석해와 잘 일치하는 것을 확인할 수 있었다.

• International Journal of Naval Architecture and Ocean Engineering
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• 제12권1호
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• pp.297-313
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• 2020

An Arctic Spar is characterized by its conical shape near the waterline. In this case, the nonlinear effects from its irregular hull shape would be significant if there is either a large amplitude floater motion or steep wave conditions. Therefore, in this paper, the nonlinear effects of an Arctic Spar are numerically investigated by introducing a weakly nonlinear time-domain model that considers the time dependent hydrostatic restoring stiffness and Froude-Krylov forces. Through numerical simulations under multiple regular and irregular wave conditions, the nonlinear behavior of the Arctic Spar is clearly observed, but it is not shown in the linear analysis. In particular, it is found that the nonlinear Froude-Krylov force plays an important role when the wave frequency is close to the heave natural frequency. In addition, the nonlinear hydrostatic restoring stiffness causes the structure's unstable motion at a half of heave natural period.

• 한국해양공학회지
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• 제23권4호
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• pp.38-46
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• 2009

Two sets of numerical simulations were carried out for a planing hull model ship. In the first, the WAVIS 1.4 linear and nonlinear potential solver was utilized with the free support condition, in which the running posture was determined during calculation. The linear and nonlinear potential calculation results showed qualitative agreement in the trim and resistance coefficient with the MOERI towing tank test. However, the nonlinear potential calculation gave better results than the linear method. In the next simulation, Fluent 6.3.26 with a VOF model and the WAVIS 1.4 nonlinear potential solver were used with the given running posture from the measurement carried out in the MOERI towing tank. Fluent with the VOF method had substantially better agreement with model test results than the results from the WAVIS nonlinear potential calculation for the total resistance coefficient, and for the bow and stern wave patterns, in spite of the much greater computational costs. Both methods can be utilized in planing hull design when their limitations are perceived, and the running posture should be predicted correctly.

• 호남수학학술지
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• 제37권4호
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• pp.411-421
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• 2015

This paper investigates the issue of analytic travelling wave solutions for some important coupled models of fractional order. Analytic travelling wave solutions of the considered model are found by means of the Q-function method. The results give us that the Q-function method is very simple, reliable and effective for searching analytic exact solutions of complex nonlinear partial differential equations.

• 한국해안해양공학회지
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• 제5권4호
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• pp.307-317
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• 1993

파랑의 비선형성 및 분산을 고려한, 연안역에서의 파랑변형에 관한 연구를 수행하였다. 규칙파의 변형에 관한 수학적 모형은 비선형 ray모델에 기초하였으며, ray 및 파동장에 관한 방정식들을 수립하였다. 비선형 파동장은 수정 Korteweg-de Vries 식으로서 나타내었으며, 이에 대한 몇몇 해석 해들을 구하였다. 또한 Caustic 변형 및 감쇄효과를 수학적 모형에 포함하였다. Korteweg-de Vries 방정식에 대한 수치계산 알고리즘과 안정조건을 기술하였으며, 연안역에서의 비선헝 파랑변형 계산 결과를 제시하였다.

• 한국해양공학회지
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• 제11권4호
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• pp.111-121
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• 1997

The spectral energy balance model is composed and the nonlinear interaction is approximated by the discrete interaction parameterization as in WAM model. The numerical results of durational limited growth test agree very well with those of the exact model, EXACT-NL. The response of a wave spectrum to a change in wind direction is investigated numerically for a sequence of direction changes 30$^{\circ}$ , 45$^{\circ}$ , 60$^{\circ}$ , 90$^{\circ}$ . The high frequency components relax more repidly to the new wind direction than the low frequency components and the relaxation process also depends on the wave age. For wind direction changes less than 60$^{\circ}$ , the coupling by nonlinear interaction is so strong that the secondary peak in input source distribution is counteracted by the negative lobe of the nonlinear interaction. For wind direction changes grater than 60$^{\circ}$ , a second independent wind-sea spectrum is generated in the new wind direction, while the old spectrum gradually decays as swell.

• 한국항만학회지
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• 제12권1호
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• pp.75-86
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• 1998

To design a coastal structure in the nearshore region, engineers must have means to estimate wave climate. Waves, approaching the surf zone from offshore, experience changes caused by combined effects of bathymetric variations, interference of man-made structure, and nonlinear interactions among wave trains. This paper has attempted to find out the effects of two of the more subtle phenomena involving nonlinear shallow water waves, amplitude dispersion and secondary wave generation. Boussinesq-type equations can be used to model the nonlinear transformation of surface waves in shallow water due to effect of shoaling, refraction, diffraction, and reflection. In this paper, generalized Boussinesq equations under the complex bottom condition is derived using the depth averaged velocity with the series expansion of the velocity potential as a product of powers of the depth of flow. A time stepping finite difference method is used to solve the derived equation. Numerical results are compared to hydraulic model results. The result with the non-linear dispersive wave equation can describe an interesting transformation a sinusoidal wave to one with a cnoidal aspect of a rapid degradation into modulated high frequency waves and transient secondary waves in an intermediate region. The amplitude dispersion of the primary wave crest results in a convex wave front after passing through the shoal and the secondary waves generated by the shoal diffracted in a radial manner into surrounding waters.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.