• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.1
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• pp.39-44
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• 2009

To improve the accuracy of numerical simulation of wave trans- formation across the surf zone, nonlinear shoaling effect based on Shuto's empirical formula and breaking mechanism are induced in the elliptic modified mild slope equation. The variations of shoaling coefficient with relative depth and deep water wave steepness are successfully reproduced and show good agreements with Shuto's formula. Breaking experiments show larger wave height distributions than linear model due to nonlinear shoaling but breaking mechanism shows a little bit larger damping in 1/20 beach slope experiment.

• Journal of the Korean Society of Marine Environment & Safety
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• v.28 no.1
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• pp.161-167
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• 2022

Ocean waves passing through the underwater bar at a shallow depth experience a shoaling effect caused by decreasing water depth, a nonlinear interaction therein owing to steepening wave slope, and a wave dispersion effect as the water depth increases again. Because this problem includes many complicated phenomena, it is used as a good example of validating a theoretical development or a CFD method for ocean wave applications. Validation is performed mainly for regular waves by comparing the wave elevation patterns in the time domain with the experimental results. In this study, the spectral evolution of wave spectrum is investigated in the frequency domain when a CFD method such as OpenFOAM is applied for this problem. In particular, the effects of initial phase conditions as well as the nonlinear interaction among harmonic waves are studied.

• 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.

• Ocean and Polar Research
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• v.30 no.4
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• pp.453-466
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• 2008

In order to examine the generation mechanism of long ocean waves along the west coast of Korea and to understand the amplification process of the long ocean waves, sea level, atmospheric pressure and wind data observed every minute from 2007 March 29 to 2007 April 1 were analyzed and onedimensional numerical ocean model experiments were performed. An atmospheric pressure jump propagated southeastward from Backryungdo to Yeonggwang along the west coast of Korea with speed of $13{\sim}27\;m/s$ between 2007 March 30 23:00 and 2007 April 1 1:30. Average magnitude of pressure jump was 4.2 hPa. As a moving atmospheric jump propagated from north to south along the coast, long ocean waves were generated and the sea level abnormally rose or fell at Anheung, Kunsan, Wido and Yeonggwang. Average amplitude of sea level rise (or fall) was about 113.6 cm. In a one-dimensional numerical ocean model, nonlinear shallow water equations were numerically integrated and a moving atmospheric pressure jump with traveling speed of 24 m/s was used as an external force. While the atmospheric pressure jump travels over 60 m depth ocean, a long ocean wave is generated. Because the propagation speed of the atmospheric jump is almost equal to that of the long ocean wave, Proudman resonance occurs and the long ocean wave amplifies. As the atmospheric pressure jump moves into the coastal area shallower than 60 m, the speed of the long ocean wave decreases and Proudman resonance effect decreases. However, the amplitude of the long ocean wave increases and wave length becomes shorter because of shoaling effect. When the long ocean wave hits the land boundary, amplitude of the long ocean wave drastically amplifies due to reflection. Data analysis and numerical experiments suggest that the southeastward propagation of an atmospheric pressure jump over the shallow ocean, which is a necessary condition for Proudaman resonance, generated the long ocean waves along the west coast of Korea on 2007 March 31 and the ocean waves amplified due to shoaling effect in the coastal area and reflection at the shore.

• Journal of Navigation and Port Research
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• v.28 no.7
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• pp.619-627
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• 2004

Introduction of wave model, considered the effect of shoaling, refraction, diffraction, partial reflection, bottom friction, breaking at the coastal waters of complex bathymetry, is a very important factor for most coastal engineering design and disaster prevention problems. As waves move from deeper waters to shallow coastal waters, the fundamental wave parameters will change and the wave energy is redistributed along wave crests due to the depth variation, the presence of islands, coastal protection structures, irregularities of the enclosing shore boundaries, and other geological features. Moreover, waves undergo severe change inside the surf zone where wave breaking occurs and in the regions where reflected waves from coastline and structural boundaries interact with the incident waves. Therefore, the application of mild-slope equation model in this field would help for understanding of wave transformation mechanism where many other models could not deal with up to now. The purpose of this study is to form a extended mild-slope equation wave model and make comparison and analysis on variation of harbor responses in the vicinities of Ulsan Harbor and Ulsan New Port, etc. due to construction of New Port in Ulsan Bay. We also considered the increase of water depth at the entrance channel by dredging work up to 15 meters depth in order to see the dredging effect. Among several model analyses, the nonlinear and breaking wave conditions are showed the most applicable results. This type of trial might be a milestone for port development in macro scale, where the induced impact analysis in the existing port due to the development could be easily neglected.

• Water for future
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• v.27 no.2
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• pp.73-83
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• 1994

The unproper development of the nearshore zone can enhance the diffusion of pollutant in the nearshore zone resulting in unbalanced sediment budget of beach which causes alteration of beach topography. Therefore, it is required to predict the effects of the envirnmental change quantitatively. In this paper, the depth-averaged and time-averaged energy balance equation is selected to acount for the wave transformation such as refraction, shoaling effect, the surf zone energy disipation, wave breaking index and bore, due to wave breaking in the shore region.(Numerical solutions are obtained by a finite difference method, ADI and Upwind. For the calculation of the wave-induced current, the unsteady nonlinear depth-averaged and time-averaged governing equation is derived based on the continuity and momentum equation for imcompressible fluid.) Numerical solutions are obtained by finite difference method considering influences of factors such as lateral mixing coefficient, bed shear stress, wave direction angle, wave steepness, wave period and bottom slope. The model is applied to the computation of wave transformation, wave-induced current and variation of mean water leel on a uniformly sloping beach.

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.527-537
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• 2003

The characteristics of ship induced waves caused by navigation become widely different from both ship's speed and water depth condition. The ship induced waves specially generated in coastwise routes frequently give rise to call unforeseen danger for swimmers and small boats as well as shoreline erosion or sea wall destruction in coastal zones. The main concern of ship induced wave study until now is either how to reduce ship resistance or how to manoeuvre the ship safely under a constant water depth in the view point of shipbuilding engineers. Moreover, due to the trends for appearance of the high speed ships at the shallow coastal water, we are confronted with the danger of damages from those ship induced waves. Therefore, it is necessary to examine the development of ship induced waves and the influence of their deformation effects according to its propagation ray. In present study, in order to predict the development of the ship induced waves and their propagation under the conditions of complicate and variable shallow water depth with varying ship's speed, we constructed a computer model using Boussinesq equation with a fixed coordinate system and verified the model results by comparison with experimental results. Additionally, the model was applied under the variable water depth based on actual passage and we then confirmed the importance of the variable water depth consideration.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.6
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• pp.409-422
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• 2019

In this study, we carried out the 3D numerical simulation to investigate the hydraulic characteristics of Synchronous Edge wave known as the driving mechanism of beach cusp using the Tool Box called the ihFoam that has its roots on the OpenFoam. As a wave driver, RANS (Reynolds Averaged Navier-Stokes equation) and mass conservation equation are used. In doing so, we materialized short-crested waves known as the prerequisite for the formation of Synchronous Edge waves by generating two obliquely colliding Cnoidal waves. Numerical results show that as can be expected, flow velocity along the cross section where waves are focused are simulated to be much faster than the one along the cross section where waves are diverged. It is also shown that along the cross section where waves are focused, up-rush is moving much faster than its associated back-wash, but a duration period of up-rush is shortened, which complies the typical characteristics of nonlinear waves. On the other hand, due to the water-merging effect triggered by the redirected flow toward wave-diverging area at the pinacle of run-up, along the cross section where waves are diverged, offshore-ward velocity is larger than shore-ward velocity at the vicinity of shore-line, while at the very middle of shoaling process, the asymmetry of flow velocity leaned toward the shore is noticeably weakened. Considering that these flow characteristics can be found without exception in Synchronous Edge waves, the numerical simulation can be regarded to be successfully implemented. In doing so, new insight about how the boundary layer streaming occur are also developed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.6
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• pp.434-449
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• 2019

In this study, we develop a new cross-shore sediment module which takes the effect of infra-gravity waves of bound mode, and boundary layer streaming on the sediment transport into account besides the well-known asymmetry and under-tow. In doing so, the effect of individual random waves occurring during the unit observation period of 1 hr on sediment transport is also fully taken into account. To demonstrate how the individual random waves would affect the sediment transport, we numerically simulate the non-linear shoaling process of random wavers over the beach of uniform slope. Numerical results show that with the consistent frequency Boussinesq Eq. the application of which is lately extended to surf zone, we could simulate the saw-tooth profile observed without exception over the surf zone, infra-gravity waves of bound mode, and boundary-layer streaming accurately enough. It is also shown that when yearly highest random waves are modeled by the equivalent nonlinear uniform waves, the maximum cross-shore transport rate well exceeds the one where the randomness is fully taken into account as much as three times. Besides, in order to optimize the free parameter K involved in the long-shore sediment module, we carry out the numerical simulation to trace the yearly shoreline change of Mang-Bang beach from 2017.4.26 to 2018.4.20 as well, and proceeds to optimize the K by comparing the traced shoreline change with the measured one. Numerical results show that the optimized K for Mang-Bang beach would be 0.17. With K = 0.17, via yearly grand circulation process comprising severe erosion by consecutively occurring yearly highest waves at the end of October, and gradual recovery over the winter and spring by swell, the advance of shore-line at the northern and southern ends of Mang-Bang beach by 18 m, and the retreat of shore-line by 2.4 m at the middle of Mang-Bang beach can be successfully duplicated in the numerical simulation.