An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion

作     者：ZHAO Hongjun SONG Zhiyao XU Fumin LI Ruijie ZHAO Hongjun1,2, SONG Zhiyao2,3, XU Fumin1,2, LI Ruijie1,2 1 Key Laboratory of Coastal Disasters and Defence, Ministry of Education, Hohai University, Nanjing 210098, China 2 Ocean College, Hohai University, Nanjing 210098, China 3 Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing 210097, China

作者机构：Key Laboratory of Coastal Disasters and Defence Ministry of Education Hohai University Nanjing 210098 China Ocean College Hohai University Nanjing 210098 China Key Laboratory of Virtual Geographic Environment Ministry of Education Nanjing Normal University Nanjing 210097 China 

出 版 物：《Acta Oceanologica Sinica》 (海洋学报（英文版）)

年 卷 期：2010年第29卷第2期

页      面：5-13页

核心收录：

学科分类：081803[工学-地质工程] 080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0818[工学-地质资源与地质工程] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Open Fund of Key Laboratory of Coastal Disasters and Defence (Ministry of Education) National Natural Science Foundation of China under contract No. 50779015 

主　　题：time-dependent mild-slope equation varying topography bottom friction nonlinear amplitude dispersion steep or rapidly wave breaking 

摘      要：In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. （2003）, the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. （2007）＇s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly varying topography and wave breaking, the present model is applied to study： （1） wave refraction and diffraction over a submerged elliptic shoal on a slope （Berkhoff et al., 1982）; （2） Bragg reflection of monochromatic waves from the sinusoidal ripples （Davies and Heathershaw, 1985）; （3） wave transformation near a shore attached breakwater （Watanabe and Maruyama, 1986）. Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models （REF/DIF model and FUNWAVE model） show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.