Nonlinear unified equations for water waves propagating over uneven bottoms in the nearshore region

被引：0

作者：

黄虎

丁平兴

吕秀红

机构：

[1] Shanghai Institute of Applied Mathematics and Mechanics

[2] Shanghai University

[3] Shanghai

[4] China State Key Laboratory of Estuarine & Coastal Research

[5] East China Normal University

[6] China

[7] State Key Laboratory of Estuarine & Coastal Research

[8] Division of Graduate Studies

来源：

ProgressinNaturalScience | 2001年 / 10期

关键词：

unified equations; Hamiltonian varlational principle for water waves; extended mild-slope equation; higher order Bousslnesq-type equations;

D O I：

暂无

中图分类号：

O302 [力学中的数学方法];

学科分类号：

0701 ;

摘要：

<正> Considering the continuous characteristics for water waves propagating over complex topography in the nearshore region, the unified nonlinear equations, based on the hypothesis for a typical uneven bottom, are presented by employing the Hamiltonian variational principle for water waves. It is verified that the equations include the following special cases: the extension of Airy"9 nonlinear shallow-water equations, the generalized mild-slope equation, the dispersion relation for the second-order Stokes waves and the higher order Boussinesq-type equations.

引用

页码：28 / 35

页数：8

共 6 条

[1]

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[2]

Derivation of the third-order evolution equations for weakly nonlinear water waves propagaing over uneve bottoms. Liu,P. L-F. et al. Wave Motion . 1989

[3]

A general wave equation for waves over rippled beds. Kirby,J. T. Journal of Fluid Mechanics . 1986

[4]

Surface waves propagation over slowly varying media of topography and non-uniform three-dimensional currents. Huang,H. et al. Progress in Natural Science . 2000

[5]

A unified model for the evolution of nonlinear water waves. Witting,J. M. Journal of Computational Physics . 1984

[6]

A unified model for periodic nonlinear dispersive waves in intermediate and shallow water. Karambas,T. V. Journal of Coastal Research . 1999

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