Sung Bum Yoon

Numerical Simulations of the 1960 Chilean Tsunami Propagation and Inundation at Hilo, Hawaii

An explicit staggered leap-frog finite difference model is used to simulate the transoceanic propagation of the 1960 Chilean tsunami and the associated inundation at Hilo, Hawaii. In computing the transoceanic tsunami propagation, linear shallow water equations with Coriolis force are solved. However, spatial grid sizes and time step sizes are chosen in such a way that the numerical dispersion introduced by the leap-frog finite difference scheme is almost the same as the frequency dispersion in the linear Boussinesq equations. Because the grid size and the time step depend on the local depth, a nested multiple-grid system is developed for the numerical model.

A MODIFIED LEAP-FROG SCHEME FOR LINEAR SHALLOW-WATER EQUATIONS

A new leap-frog finite difference scheme is proposed to solve the linear shallow-water equations. The accuracy of propagation speed in diagonal direction is improved through the inclusion of freque...

Numerical Study on Sea State Parameters Affecting Rip Current at Haeundae Beach : Wave Period, Height, Direction and Tidal Elevation

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.

A NOTE ON EXTENSION OF FULLY DISPERSIVE WEAKLY NONLINEAR WAVE EQUATIONS FOR RAPIDLY VARYING TOPOGRAPHY

Following the approach proposed by Nadaoka et al. [Nadaoka, K., Beji, S. and Nakagawa, Y. (1997) A fully dispersive weakly nonlinear model for water waves, Proc. Roy. Soc. London A453, pp. 303–318], we present a set of one-dimensional weakly nonlinear single-component wave equations for rapidly varying topography by including the bottom curvature and squared bottom slope terms ignored in the original equations of Nadaoka et al. To solve the linear version of the extended wave equations derived in this study, a finite difference numerical model is constructed. The performance of the model is tested for the case of wave reflection from a plane slope and a rippled bed. Numerical results Eire compared with those calculated using other numerical models reported earlier. It is shown that the accuracy of the present numerical model is improved significantly in comparison with that of the original equations of Nadaoka et al. by including a complete set of higher order bottom effect terms for a rapidly varying topography.

Understanding of Rip Current Generation Mechanism at Haeundae Beach of Korea: Honeycomb Waves

ABSTRACT Shin, C.H.; Noh, H.K.; Yoon, S.B., and Choi, J., 2014. Understanding of rip current generation mechanism at Haeundae Beach of Korea: Honeycomb waves. Many studies have proposed the generation mechanism of rip currents observed at Haeundae beach. Most of them suspect the rip channels as a rip current generating mechanism at this beach. This study focuses on the understanding of rip current generation mechanism in a different point of view based on the CCTV images and the numerical simulations. The CCTV images captured when the rip currents occurred show that the rip currents are accompanied by the waves of honeycomb pattern. The rip currents are developed along the nodal lines of honeycomb waves. To confirm the new mechanism of rip current generation at Haeundae Beach a series of numerical experiments are conducted using a phase resolving numerical model based on the nonlinear Boussinesq equations. The numerical results with the simplified beach topography and the incident honeycomb waves similar to real ones show that the rip currents can be generated without the rip channels. The rip currents generated by the honeycomb waves can grow much faster and the intensity of the rip currents is much stronger than those generated by the unidirectional waves over the rip channels. The magnitude of rip currents agrees reasonably well with that observed using CCTV image analyses. The role of rip channels developed by the rip currents is also discussed.

Surface Roller Modeling for Mean Longshore Current over a Barred Beach in a Random Wave Environment

Abstract Choi, J.; Lee, J.-I., and Yoon, S.B., 2012. Surface roller modeling for mean longshore current over a barred beach in a random wave environment. The effect of surface roller on mean longshore current, which depends strongly on the wave-breaking process, was investigated by applying various surface-roller models to a random wave-induced current-model system, incorporating a nearshore circulation model, SHORECIRC, and a random wave model, SWAN. The investigation was performed based on simulations of the SandyDuck field experiments, employing observed wave spectra and two-dimensional topography. The topography is characterized as a longshore variation caused by scouring because of bridge piers and a barred beach on a steep foreshore slope linked to a relatively broad bar formation on a seaward gentle slope. The experimental data show that before the waves intensely broke from a decrease in water depth on the steep slope, some partial breaking of random waves occurred in the wave-breaking process. The chosen surface-roller model was modified using the classification of the partial wave-breaking and intense wave-breaking regions. The mean longshore currents simulated using the modified surface-roller model was compared with the measurements as well as the results from the simulations using conventional surface-roller models. The modified simulations agreed with the measurements better than did those of the simulations.

TSUNAMI INUNDATION SIMULATION OF A BUILT-UP AREA USING EQUIVALENT RESISTANCE COEFFICIENT

An equivalent resistance coefficient that includes the effect of drag caused by buildings as well as the bottom friction effect was investigated for two-dimensional inundation simulation of built-up areas with relatively coarse grids. In order to quantify the equivalent resistance coefficient for a given built-up area, we performed laboratory experiments and three-dimensional numerical experiments of steady and uniform flows influenced by square unsubmerged piers spaced at equal intervals in the longitudinal and transverse directions. The Mannings n, which represents the equivalent resistance coefficient, was evaluated by inputting experimental data into the Mannings equation. A semi-analytical formula for the n value under experimental conditions was derived via momentum analysis that included drag interaction effects. The n values resulting from laboratory experimental data, the three-dimensional numerical data, and the semi-analytical formula agreed well with each other. From these results, we found that the equivalent resistance coefficient n value is strongly dependent on the intervals between piers and increases according to water depth to the 2/3 power. In addition, as an application of the proposed n formula to the inundation model, we performed a simulation of a tsunami inundation on Imwon Harbor on the east coast of Korea.

Study of Rip Current Warning Index Function Varied according to Real-time Observations

A rip-current warning index function, which is estimated from the likelihood of rip current quantified based on numerical simulations under various sea environments and is varied according to real-time buoy-observations, was studied to help protect against rip current accidents at Haeundae beach. For the quantification, the definition of likelihood of rip current, which proposed by Choi et al. (2011, 2012b), was employed and estimated based on Boussinesq modelling. The distribution of likelihood of rip current was evaluated by using various simulations according to scenarios established based on physical quantities(i.e., wave parameters) of buoy-observations. To index the likelihood of rip current, empirical functions were derived based on the distribution and adjusted to observational environments. In this study, the observations from June to September in 2011 at Haeundae beach were applied to the rip-current index functions, and its applications into the real events found based on CCTV images were presented and investigated. In addition, limitations and improvements of the rip-current index function were discussed.

A DISPERSION-CORRECTED FINITE ELEMENT MODEL FOR SIMULATION OF DISTANT TSUNAMIS

A dispersion-corrected finite element model is developed to simulate the propagation of distant tsunamis over a slowly varying topography. A linear Boussinesq wave equation is solved to consider the dispersion effect of tsunami waves by employing a linear triangular mesh and an explicit time integration scheme. The numerical dispersion associated with the explicit scheme is minimized by adjusting both the mesh size and the dispersion-correction parameter. In order to test the present model, numerical simulations for the propagation of an initial Gaussian hump over various constant depths are conducted, and the numerical results are compared with analytical solutions of the linear Boussinesq equations. The present model is also tested for the propagation of tsunamis over a submerged circular shoal and the numerical results are compared with the numerical solutions obtained using another Boussinesq model. The present model is shown to be efficient and considerably accurate.

Tsunami research in Korea

The tsunamis that have occurred in many places around the world over the past decades have taken a heavy toll on human lives and property. The eastern coast of the Korean Peninsula is not safe from tsunamis and has sustained tsunami damage in the past. The aim of this study is to review the past, present, and future of some aspects of tsunami research in Korea. A composite numerical model comprising propagation and inundation models is described. The paper also covers tsunami mitigation efforts in Korea, and a tsunami hazard map is developed and introduced.