广义缓坡方程

黄虎; 丁平兴; 吕秀红

广义缓坡方程

1.
华东师范大学河口海岸国家重点实验室, 上海200062;
2.
上海大学上海市应用数学和力学研究所, 上海200072

基金项目: 国家杰出青年科学基金资助项目(49825161);1999年上海市博市后科研资助计划资助

详细信息

作者简介:
黄虎(1964- ),男,新疆石河子人,副教授,博士.

中图分类号: O353.2
计量
- 文章访问数: 2485
- HTML全文浏览量: 100
- PDF下载量: 809
- 被引次数: 0
出版历程
- 收稿日期: 1999-07-30
- 修回日期: 2001-01-15
- 刊出日期: 2001-06-15

Extended Mild-Slope Equation

1.
State Key Laboratory of Estuarine & Coastal Research, East China Normal University, Shanghai 200062, P R China;
2.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China

摘要

摘要: 运用表面波Hamilton方法和缓坡逼近假定,分析缓变三维流场和非平整海底对波浪传播的影响,推导出广义缓坡方程。海底地形由两个分量组成:慢变分量,其水平长度尺度大于表面波的波长;快变分量,其振幅与表面波的波长相比为一小量,但是其频率与表面波频率相当。该广义缓坡方程具有广泛的适用范围,以下著名的缓坡方程成为它的特例:经典的Berkhoff缓坡方程;包含环境流效应的Kirby缓坡方程;描述波状海底特征的Dingemans缓坡方程。另外,同时也得到了描述环境流场和快变海底效应的广义浅水方程。
- 缓坡方程 /
- 缓变三维流 /
- 快变海底 /
- 表面波的Hamilton方法
Abstract: The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom,thus leading to an extended mild-slope equation.The bottom topography consists of two components:the slowly varying component whose horizontal length scale is longer than the surface wave length,and the fast varying component with the amplitude being smaller than that of the surface wave.The frequency of the fast varying depth component is,however,comparable to that of the surface waves. The extended mild-slope equation is more widely applicable and contains as special cases famous mild-slope equations below:the classical mild-slope equation of Berkhoff,Kirby.s mild-slope equation with current,and Dingemans.s mild-slope equation for rippled bed.The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.
- mild-slope equation /
- slowly varying three-dimensional currents /
- rapidly varying topography /
- Hamiltonian formalism for surface waves

HTML全文

参考文献(14)

[1]	Dingemans M W. Water Wave Propagatio n Over Uneven Bottoms[M]. Singapore: World Scientific,1997.
[2]	Kirby J T. Nonlinear, dispersive long waves in water of va riable depth[A]. In: Hunt J N Ed. Gravity Waves in Water of Finite Depth[C]. Southampt on: Computational Mechanics Publications,1997,55-126.
[3]	Kirby J T. A note on linear surface wave-current interaction[J]. J Geophys Res,1984,89(C1):745-747.
[4]	Yoon S B, Liu P L-F. Interaction of currents and weakly no nlinear water waves in shallow water[J]. J Fluid Mech,1989,205:397-419.
[5]	Liu P L-F. Wave transformation[A]. In: LeMehaute B, Hane s D M Ed s. The Sea, Ocean Engineering Science[C]. New York: J Wiley and Sons,1990, 27-63.
[6]	Kirby J T. A general wave equation for waves over rippled beds[J]. J Fluid Mech,1986,162:171-186.
[7]	Chamberlain P G, Porter D. The modified mild-slope equation[J]. J Fluid Mech,1995,291:393-407.
[8]	Chandrasekera C N, Cheung K F. Extended linear refraction-diffraction model[J]. J Wtrwy Port Coast and Oc Engrg,1997,123(5) :280-286.
[9]	Lee C, Park W S, Cho Y-S, et al. Hyperbolic mild-slope equations extended to account for rapidly varying topography[J]. Coastal Eng,1998,34:243-257.
[10]	Thomas G P, Klopman G. Wave-current interactions in the near shore region[A]. In: Hunt J N Ed. Gravity Waves in Water of Finite Depth[C]. Southampton: Computational Mechanics Publications,1997,255-319.
[11]	Zakharov V E. Stability of periodic waves of finite amplitude on the surface of a deep fluid[J]. J Appl Mech Tech Phys,1968,2:190-194.
[12]	Broer L J F. On the Hamiltonian theory of surface waves[J]. Appl Sci Res,1974,30(5):430-446.
[13]	Miles J W. On Hamilton's principle for surface waves[J]. J Fluid Mech,1977,83:153-158.
[14]	Berkhoff J C W. Computation of combined refraction-diffraction[A]. In: 13th Inte Conf on Coastal Engng[C]. New York: ASCE,1972,471-490.