• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.1
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• pp.121-127
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• 2008

Numerical experiments with weakly nonlinear MIKE21 BW module and fully nonlinear FUNWAVE model are performed to identify the nonlinear characteristics of Boussinesq models with varying nonlinearity. Generation of waves with varying amplitudes, nonlinear shoaling and wave propagation over submerged bar experiments showed the importance of nonlinear model in shallow water where nonlinearity becomes prominent. Fully nonlinear model showed the nonsymmetrical wave form more clearly and gave larger shoaling coefficients than those of weakly nonlinear model.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 1998.10a
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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.

• Ocean Systems Engineering
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• v.2 no.3
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• pp.189-203
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• 2012

New experiments focusing on the evolution characteristics of nonlinear wave trains were conducted in a large wave flume. A series of wave trains with added sidebands, varying initial steepness, perturbed amplitudes and frequencies, were physically generated in a long wave flume. The experimental results show that the increasing wave steepness, increases the speed of sidebands growth. To study the frequency and phase modulation, the Morlet wavelet transform is adopted to extract the instantaneous frequency of wave trains and the phase functions of each wave component. From the instantaneous frequency, there are local frequency downshifts, even an effective frequency downshift was not observed. The frequency modulation increases with an increase in amplitude modulation, and abrupt changes of instantaneous frequencies occur at the peak modulation. The wrapped phase functions show that in the early stage of the modulation, the phase of the upper sideband first diverges from that of the carrier waves. However, at the later stage, the discrepancy phase from the carrier wave transformed to the lower sideband. The phase deviations appear in the front of the envelope's peaks. Furthermore, the evolution of the instantaneous frequency exhibits an approximate recurrence-type for the experiment with large imposed sidebands, even when the corresponding recurrence is not observed in the Fourier spectrum.

• Journal of the Korean Society for Nondestructive Testing
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• v.30 no.5
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• pp.458-463
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• 2010

Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions; (1) phase matching, (2) non-zero power flux, (3) group velocity matching, and (4) non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter growed up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters.

• Journal of the Society of Naval Architects of Korea
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• v.60 no.5
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• pp.341-350
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• 2023

In this paper, numerical experiments are performed to examine the collision between a solitary wave and a wave-packet (dispersive wave) in shallow water. We attempt to introduce the improved Boussinesq equation governing the experiments, which is solved by using a semi-analytical approach, called Pseudo-parameter Iteration method(PIM). Using various numerical experiments, we have observed that the wave-packet (propagating dispersive wave) experiences a phase shift after collision with a solitary wave. This phenomenon may be considered as a nonlinear wave-wave interaction in shallow water.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2000.04a
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• pp.140-145
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• 2000

The spectral method which is composed of an eigenfunction expansion of free modes in the wave number domain is used to produce two dimensional unsteady inviscid wave simulation such as progressive waves in a numerical pneumatic wave tank. A spatial and time dependent free surface elevation and the potential are calculated by integrating ODE derived from fully nonlinear kinematic and dynamic free surface boundary condition at each time step. The nonlinear characteristics in the waves by this method were notable as increasing wave steepness. This method is very useful and powerful in terms of saving computational time caused by rapid convergence exponentially with increasing number of nodes, even preserving accurate numerical results. Moreover, it will given us many possibilities to apply to naval and ocean engineering fields.

• Ocean Systems Engineering
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• v.9 no.3
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• pp.219-240
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• 2019

This paper presents the comparison between SFT response with linear and nonlinear cables. The dynamic response analysis of submerged floating tunnel (SFT) is presented computationally with linear and nonlinear tension legs cables. The analysis is performed computationally for two wave directions one at 90 degrees (perpendicular) to tunnel and other at 45 degrees to the tunnel. The tension legs or cables are assumed as linear and non- linear and the analysis is also performed by assuming one tension leg or cable is failed. The Response Amplitude Operators (RAO's) are computed for first order waves, second order waves for both failure and non-failure case of cables. For first order waves- the SFT response is higher for sway and heave degree of freedom with nonlinear cables as compared with linear cables. For second order waves the SFT response in sway degree of freedom is bit higher response with linear cables as compared with nonlinear cables and the SFT in heave degree of freedom has higher response at low time periods with nonlinear cables as compared with linear cables. For irregular waves the power spectral densities (PSD's) has been computed for sway and heave degrees of freedom, at $45^0$ wave direction PSD's are higher with linear cables as compared with nonlinear cables and at $90^0$ wave direction the PSD's are higher with non-linear cables. The mooring force responses are also computed in y and z directions for linear and nonlinear cables.

• Journal of the Korean Society for Nondestructive Testing
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• v.29 no.4
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• pp.344-350
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• 2009

The goal of this study is to introduce the theoretical background of acoustic nonlinearity in surface wave and to verify its characteristics by experiments. It has been known by theory that the nonlinear parameter of surface wave is proportional to the ratio of $2^{nd}$ harmonic amplitude and the power of primary component in the propagated surface wave, as like as in bulk waves. In this paper, in order to verify this characteristics we constructed a measurement system using contact angle beam transducers and measured the nonlinear parameter of surface wave in an Aluminum 6061 alloy block specimen while changing the distance of wave propagation and the input amplitude. We also considered the effect of frequency-dependent attenuation to the measurement of nonlinear parameter. Results showed good agreement with the theoretical expectation that the nonlinear parameter should be independent on the input amplitude and linearly dependent on the input amplitude and the $2^{nd}$ harmonic amplitude is linearly dependant on the propagation distance.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.393-410
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• 2015

Two dimensional numerical models and physical models have been developed to study the highly nonlinear interactions between waves and breakwaters, but several of these models consider the effects of the structural dynamic responses and the shape of the breakwater axis on the wave pressures. In this study, a multi-material Arbitrary Lagrangian Eulerian (ALE) method is developed to simulate the nonlinear interactions between nonlinear waves and elastic seawalls on a coastal rubble mound breakwater, and is validated experimentally. In the experiment, a solitary wave is generated and used with a physical breakwater model. The wave impact is validated computationally using a breakwater - flume coupling model that replicates the physical model. The computational results, including those for the wave pressure and the water-on-deck, are in good agreement with the experimental results. A local breakwater model is used to discuss the effects of the structural dynamic response and different design parameters of the breakwater on wave loads, together with pressure distribution up the seawall. A large-scale breakwater model is used to numerically study the large-scale wave impact problem and the horizontal distribution of the wave pressures on the seawalls.

• Journal of Korean Port Research
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• v.12 no.1
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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.