Modeling of 500-year tsunamis for probabilistic design of coastal infrastructure in the Pacific Northwest

This paper describes the development of tsunami scenarios from the National Seismic Hazard Maps for design of coastal infrastructure in the Pacific Northwest. The logic tree of Cascadia earthquakes provides four 500-year rupture configurations at moment magnitude 8.8, 9.0, and 9.2 for development of probabilistic design criteria. A planar fault model describes the rupture configurations and determines the earth surface deformation for tsunami modeling. A case study of four bridge sites at Siletz Bay, Oregon illustrates the challenges in modeling of tsunamis on the Pacific Northwest coast. A nonlinear shallow-water model with a shock-capturing scheme describes tsunami propagation across the northeastern Pacific as well as barrier beach overtopping, bore formation, and detailed flow conditions at Siletz Bay. The results show strong correlation with geological evidence from the six paleotsunamis during the last 2800 years. The proposed approach allows determination of tsunami loads that are consistent with the seismic loads currently in use for design of buildings and structures.     

High-resolution central difference scheme for the shallow water equations

1 IntroductionThe shallow water equations (SWE) are frequent-ly used as a mathematical model for water flows incoastal areas, lakes, estuaries, etc. Thus, they are animportant tool to simulate a variety of problems relat-ed to coastal engineering, environment, ecology, etc.(Bermúdez et al., 1998). On the basis of solving theone-dimensional (1D) SWE, Hu et al. (2000) have de-veloped a model capable of simulating storm wavespropagating in the coastal surf zone and overtopping asea wall. Ano…     

A note on linear dispersion and shoaling properties in extended Boussinesq equations

A set of optimum parameter α is obtained to evaluate the linear dispersion and shoaling properties in the extended Boussinesq equations of [Madsen and Sorensen, 1992 and Nwogu, 1993], and [Chen and Liu, 1995]. Optimum α values are determined to produce minimal errors in each wave property of phase velocity, group velocity, or shoaling coefficient relative to the analytical one given by the Stokes wave theory. Comparisons are made of the percent errors in phase velocity, group velocity, and shoaling coefficient produced by the Boussinesq equations with a different set of optimum α values. The case with a fixed value of α = −0.4 is also presented in the comparison. The comparisons reveal that the optimum α value tuned for a particular wave property gives in general poor results for other properties. Considering all the properties simultaneously, the fixed value of α = −0.4 may give overall accuracies in phase velocity and shoaling coefficient for all the types of Boussinesq equations selected in this study.     

A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations

A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments.     

On an improvement of a nonlinear iterative scheme for nonlinear wave profile prediction

The authors of the present paper present an iterative scheme to calculate the nonlinear wave profiles [Jang, T.S., Kwon, S.H., 2005. Application of nonlinear iteration scheme to the nonlinear water wave problem: Stokian wave. Ocean Engineering, in press]. The nonlinear operator was constructed from the dynamic boundary condition of the free surface. The initial input of the iterative process was linear potential. The linear dispersion relation was utilized. The authors of the present paper suggest an improved scheme in terms of accuracy and speed of convergence by utilizing the nonlinear dispersion relation. The existence and uniqueness of the improved scheme are illustrated in this paper. The calculation results together with Fast Fourier transform revealed that the improved scheme made it possible to predict higher-order nonlinear characteristics of the Stokes’ wave.     

关于Boussinesq型水波方程理论和应用研究的综述

Boussinesq型方程是研究水波传播与演化问题的重要工具之一,本文就1967-2018年常用的Boussinesq型水波方程从理论推导和数值应用两个方面进行了回顾,以期推动该类方程在海岸(海洋)工程波浪水动力方向的深入研究和应用。此类方程推导主要从欧拉方程或Laplace方程出发。在一定的非线性和缓坡假设等条件下,国内外学者建立了多个Boussinesq型水波方程,并以Stokes波的相关理论为依据,考察了这些方程在相速度、群速度、线性变浅梯度、二阶非线性、三阶非线性、波幅离散、速度沿水深分布以及和(差)频等多方面性能的精度。将Boussinesq型水波方程分为水平二维和三维两大类,并对主要Boussinesq型水波方程的特性进行了评述。进而又对适合渗透地形和存在流体分层情况下的Boussinesq型水波方程进行了简述与评论。最后对这些方程的应用进行了总结与分析。