Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem

A series of laboratory experiments was carried out to investigate the strong reflection of regular water waves over a train of submerged breakwaters. Rectangular and trapezoidal shapes of submerged breakwaters are employed and compared for reflecting capability of incident waves. Measured reflection coefficients of regular waves over impermeable submerged breakwaters are verified by comparing with those of the eigenfunction expansion method. A very good agreement is observed. Reflection coefficients of permeable submerged breakwaters are less than those of impermeable breakwaters. The trapezoidal shape is recommended for a submerged breakwater in terms of reflecting capability and practical application.     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

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.     

Propagation and run-up of nearshore tsunamis with HLLC approximate Riemann solver

A numerical model describing the propagation and run-up process of nearshore tsunamis in the vicinity of shorelines is developed based on an approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using a finite volume method. The nonlinear terms in the momentum equations are solved with the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver. The developed model is first applied to prediction of water motions in a parabolic basin, and propagation and subsequent run-up process of nearshore tsunamis around a circular island. Computed results are then compared with available analytical solutions and laboratory measurements. Very reasonable agreements are observed.     

An integrated Bayesian approach to the probabilistic tsunami risk model for the location and magnitude of earthquakes: application to the eastern coast of the Korean Peninsula

We explored the distributional changes in tsunami height along the eastern coast of the Korean Peninsula resulting from virtual and historical tsunami earthquakes. The results confirm significant distributional changes in tsunami height depending on the location and magnitude of earthquakes. We further developed a statistical model to jointly analyse tsunami heights from multiple events, considering the functional relationships; we estimated parameters conveying earthquake characteristics in a Weibull distribution, all within a Bayesian regression framework. We found the proposed model effective and informative for the estimation of tsunami hazard analysis from an earthquake of a given magnitude at a particular location. Specifically, several applications presented in this study showed that the proposed Bayesian approach has the advantage of conveying the uncertainty of the parameter estimates and its substantial effect on estimating tsunami risk.     

Linear wave reflection by trench with various shapes

Two types of analytical solutions for waves propagating over an asymmetric trench are derived. One is a long-wave solution and the other is a mild-slope solution, which is applicable to deeper water. The water depth inside the trench varies in proportion to a power of the distance from the center of the trench (which is the deepest water depth point and the origin of x-coordinate in this study). The mild-slope equation is transformed into a second-order ordinary differential equation with variable coefficients based on the longwave assumption [Hunt's, 1979. Direct solution of wave dispersion equation. Journal of Waterway, Port, Coast. and Ocean Engineering 105, 457–459] as approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed.     

Two-dimensional wave-current interaction with a locally enriched quadtree grid system

Wave-induced currents may drive nearshore mixing and transport processes, including coastal pollutant dispersion, littoral drift, and long-term morphological changes through beach erosion and accretion. In this study, a numerical model is newly developed to simulate wave climate and localized currents in complicated coastal environments. The model developed is based on a quadtree grid system. The two-dimensional hydrodynamic governing equations are solved by using an explicit Adams-Bashforth finite difference scheme. Effects of wave breaking, shoaling, refraction, diffraction, wave-current interaction, set-up and set-down, turbulent mixing, bed friction, and shoreline movement are incorporated in the model. Results are presented for set-up at a beach in a flume due to normally incident waves, and longshore currents generated by oblique waves on a plane beach.     

Finite element method for strong reflection of water waves

In this study, the propagation of monochromatic water waves over an arbitrarily varying topography is numerically investigated. A finite element model is developed by formulating the diffraction of waves caused by depth changes. Not only the propagating mode but also the evanescent modes are included in the model. The model developed is applied to the study of strong reflection of monochromatic waves over a sinusoidally varying topography. Predicted reflection coefficients are compared with those of available laboratory experiments and the eigenfunction expansion method. A very good agreement is observed.     

Best-fit distribution and log-normality for tsunami heights along coastal lines

The best-fit distribution of the tsunami height was investigated along the Eastern Coast of Korean Peninsula. Firstly, the tsunami heights corresponding to the nine probable undersea earthquakes were obtained along the coastline using the numerical simulation. The method of L-moment ratio diagram was used to identify the best-fit probability density function of the tsunami heights caused by each undersea earthquake. The result indicates the generalized Pareto distribution is the best-fit distribution representing the tsunami heights regardless of the characteristics of the undersea earthquakes. This is particularly because the area of high tsunami heights and its relative magnitude to the adjacent locations were similar for the most simulations cases. In addition, this study further investigated the reason why the tsunami height distribution is not represented by the log-normal (LN) distribution as suggested by the previous studies. Result of the investigation indicates that the log-normality of the tsunami heights can be preserved when the length of a coastal line is not long such that the homogeneity of the length of the wave propagation paths reaching at different locations of the coastal line is preserved. This subsequently secures the central limit theorem making the distribution of the tsunami heights have the LN distribution. As the length of the coastal line increases, the deviation of the tsunami height distribution from the log-normality increases.     

Practical modified scheme of linear shallow-water equations for distant propagation of tsunamis

A simple but practical numerical model describing a distant propagation of tsunamis is newly proposed by introducing an additional term to the existing modified scheme. The numerical dispersion of the proposed model is manipulated to replace the physical dispersion of the linear Boussinesq equations without any limitation. The new model developed in this study is applied to propagation of a Gaussian hump over a constant water depth and the predicted free surface displacements are compared with available analytical solutions. A very reasonable agreement is observed.