| An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion |
| |
| 作者姓名： | ZHAO Hongjun SONG Zhiyao XU Fumin LI Ruijie |
| |
| 作者单位： | ZHAO Hongjun,XU Fumin,LI Ruijie(Key Laboratory of Coastal Disasters and Defence,Ministry of Education,Hohai University,Nanjing 210098,China;Ocean College,Hohai University,Nanjing 210098,China);SONG Zhiyao(Ocean College,Hohai University,Nanjing 210098,China;Key Laboratory of Virtual Geographic Environment,Ministry of Education,Nanjing Normal University,Nanjing 210097,China) |
| |
| 基金项目： | Open Fund of Key Laboratory of Coastal Disasters and Defence (Ministry of Education) and National Natural
Science Foundation of China under contract No. 50779015. |
| |
| 摘 要： | In the present paper, by introducing the effective wave elevation, we transform the extended ellip- tic 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 vary- ing 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.
|
| 关 键 词： | 椭圆型缓坡方程 数值模型 时间依赖性 非线性方程 色散关系 振幅 布拉格反射 WAVE模型 |
| 收稿时间： | 2009/1/15 0:00:00 |
| 修稿时间： | 2009/11/10 0:00:00 |
An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion |
| |
| ZHAO Hongjun,SONG Zhiyao,XU Fumin,LI Ruijie.An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion[J].Acta Oceanologica Sinica,2010,29(2):5-13. |
| |
| Authors: | ZHAO Hongjun SONG Zhiyao XU Fumin and LI Ruijie |
| |
| Institution: | 1.Key Laboratory of Coastal Disasters and Defence, Ministry of Education, Hohai University, Nanjing 210098, China;Ocean College, Hohai University, Nanjing 210098, China2.Ocean College, Hohai University, Nanjing 210098, China;Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing 210097, China |
| |
| Abstract: | In the present paper, by introducing the effective wave elevation, we transform the extended ellip-
tic 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 vary-
ing 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. |
| |
| Keywords: | time-dependent mild-slope equation nonlinear amplitude dispersion steep or rapidly
varying topography bottom friction wave breaking |
| 本文献已被 CNKI 维普 万方数据 SpringerLink 等数据库收录！ |
| 点击此处可从《海洋学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《海洋学报(英文版)》下载免费的PDF全文 |
|
