• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.12 no.4
• /
• pp.181-189
• /
• 2000

A weakly nonlinear mild-slope equation has been derived directly from the continuity equation with the aid of the Galerkin's method. The equation is combined with the momentum equations defined at the mean water level. A single component model has also been obtained in terms of the surface displacement. The linearized form is completely identical with the time-dependent mild-slope equation proposed by Smith and Sprinks(1975). For the verification purposes of the present nonlinear model, the degenerate forms were compared with Airy(1845)'s non-dispersive nonlinear wave equation, classical Boussinesq equation, andsecond¬order permanent Stokes waves. In this study, the present nonlinear wave equations are discretized by the approximate factorization techniques so that a tridiagonal matrix solver is used for each direction. Through the comparison with physical experiments, nonlinear wave model capacity was examined and the overall agreement was obtained.

• Journal of Korean Port Research
• /
• v.12 no.1
• /
• pp.75-86
• /
• 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.

• Journal of Korea Water Resources Association
• /
• v.46 no.2
• /
• pp.205-218
• /
• 2013

The likelihood of rip current at Haeundae beach according to wave parameters, such as wave height, period, direction, and tidal elevation, was estimated by using numerical simulations with a Boussinesq model, FUNWAVE. To examine the estimation, the rip current occurred on 12th June, 2011 at Haeundae beach was simulated based on observations. For the estimation, the following procedure was carried out. First, extensive numerical simulations of nearshore circulations are performed under various random sea conditions according to the wave parameters. Second, from the numerical results, cross shore components of two-wave-period averaged velocities over the nearshore area were computed, and their seawardly maximum was defined as rip current velocity of the area. Third, using time series of the rip current velocity, we computed the ratio of the simulation time and the time period in which the rip current velocity exceed a threshold velocity for rip-current accidents, and thus the ratio was quantified as the likelihood of rip current at Haeundae beach for the input wave parameters. From the resultant estimations, it was found that the rip current likelihood increases as wave height and period increase, and tidal elevation decreases.

• Journal of Navigation and Port Research
• /
• v.27 no.5
• /
• pp.527-537
• /
• 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
• /
• v.21 no.2
• /
• pp.108-116
• /
• 2009

The present study introduces a Legendre interpolation function which is capable of analyzing wave transformation effectively in a finite element method. A Lagrangian interpolation function has been mostly used for a finite element method with a higher-order interpolation function. Although this function has an advantage of giving an accurate result with less number of elements, simulation time increases. Calculation time can be reduced by mass lumping, whereas the accuracy of solution is lowered. In this study, we introduce a modified Lagrangian interpolation function, Legendre cardinal interpolation, which can reduce simulation time with keeping up favorable accuracy. Through various numerical simulations using a Boussinesq equations model, the superiority of the Legendre cardinal interpolation function to a Lagrangian interpolation function was shown.

• Journal of the Society of Naval Architects of Korea
• /
• v.39 no.1
• /
• pp.38-48
• /
• 2002

Theoretical development to generate the directional extreme waves in model basin is established based on wave focusing method. The effects of associated parameters, such as the directional range, frequency width, and center frequency, are investigated in terms of wave focusing efficiency. The two different spectral models of constant wave amplitude and constant wave slope are applied to control the wave characteristics. The wave packets simulated by theory are compared with numerical results based on Boussinesq equation and FEM. Both controls of direction and frequency spectrum are essential to focus directional waves effectively. It is noticed that wave focusing ability depends on the frequency bandwidth of spectrum rather than center frequency, and both spectral models with same parameters result in the equivalent efficiency of wave focusing.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.32 no.5B
• /
• pp.321-329
• /
• 2012

Two regular progressive wave trains, the directions of which are slightly different from each other, develop a honeycomb pattern of wave crests due to their nonlinear interaction. In the honeycomb pattern of wave crest, the nodal line area, which has very low wave energy, is formed. When the honeycomb pattern is developed near the beach area, rip current evolves through the nodal line area formed in the cross shore direction. In this study, to confirm that the formation of honeycomb pattern of waves near the beach area is a dominant mechanism of rip current occurred at Haeundae beach, we performed a numerical simulation of nearshore circulation at Haeundae beach under an unidirectional and monochromatic wave condition by using a nonlinear Boussinesq equation model. As a result, wave refraction due to topographical characteristics (i.e., submerged shoal) of Haeundae gave rise to several wave trains propagating with slightly different directions toward the beach, and consequently rip currents well developed through the nodal line area of honeycomb patterns of wave crest. In addition, we found that a narrow-banded spectral wave condition (i.e., a swell spectrum) increases more likelihood of rip current than a broad-banded spectral wave condtion based on the simulations employing various wave spectra with an equivalent wave height and period.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.2 no.1
• /
• pp.51-57
• /
• 1990

Based on second-order Stokes wave and parabolic approximation, a refraction-diffraction model for linear and nonlinear waves is developed. With the assumption that the water depth is slowly varying, the model equation describes the forward scattered wavefield. The parabolic approximation equations account for the combined effects of refraction and diffraction, while the influences of bottom friction, current and wind have been neglected. The model is tested against laboratory experiments for the case of submerged circular shoal, when both refraction and diffraction are equally significant. Based on Boussinesq equations, the parabolic approximation eq. is applied to the propagation of shallow water waves. In the case without currents, the forward diffraction of Cnoidal waves by a straight breakwater is studied numerically. The formation of stem waves along the breakwater and the relation between the stem waves and the incident wave characteristics are discussed. Numerical experiments are carried out using different bottom slopes and different angles of incidence.

• Journal of Navigation and Port Research
• /
• v.30 no.2
• /
• pp.125-130
• /
• 2006

Waves, which are the main source of ship motions in a seaway, considerably affect the performance of a ship. The study of waves and their impact on ship motions within harbors is an important aspect of the design and operation of harbors. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor. Such a prediction makes it possible to evaluate ship safety more accurately. The wave transformation model reported here is applied to actual ports based on Boussinesq wave equations both non-linear and dispersive wave processes be considered in order to capture physical effects such as wave shoaling, refractions, reflection and diffraction in variable depth environments. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor, Such a prediction makes it possible to evaluate ship safety more accurately and provide safe wave informations for navigation. Furthermore, a wave information support system is proposed for entering ships as one technique for improving the safety of ship operations. This system predicts the run of waves and reduces the danger by identifying the most dangerous point near the harbor entrance at the small wave groups.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.34 no.6
• /
• pp.177-187
• /
• 2022

This study estimates the design wave in the event of a typhoon attack at Busan new port using the wind field, the revised shallow water design wave estimation method proposed by the Ministry of Oceans and Fisheries in 2020, and proposed a reliable method of calculating the shallow water design through verification with the wave observation data. As a result of estimating typhoon wave using the wind field and SWAN numerical model, which are commonly used in the field work, for typhoon that affected Busan new port, it was found that reproducibility was not good except typhoons KONG-REY(1825) and MAYSAK(2009). In particular, in the case of typhoon MAEMI(0314), which had the greatest impact on Busan new port, the maximum significant wave height was estimated to be about 35.0% smaller than that of the observed wave data. Therefore, a plan to improve the reproducibility of typhoon wave was reviewed by applying the method of correcting the wind field and the method of using the Boussinesq equation numerical model, respectively. As a result of the review, it was found that the reproducibility of the wind field was not good as before when the wind field correction. However as a method of linking wind field data, SWAN model results, and Boussinesq numerical model, typhoon wave was estimated during typhoon MAEMI(0314), and the maximum significant wave was similar to the wave observations, so it was reviewed to have good reproducibility.