缓变深度分层流体中的准周期波和准孤立波
Quasi-Periodic Waves and Quasi-Solitary Waves in Stratified Fluid of Slowly Varying Depth
-
摘要: 本文讨论具缓变深度二流体系统中的非线性波,该系统由一不规则底部与一水平固壁间的两层常密度无粘流体所组成.文中用约化摄动法导出了所考虑模型的变系数Korteweg-de Vries方程,并用多重尺度法求出了该方程的近似解,发现底部固壁的不规则变化将产生所谓准周期波和准孤立波.它们的周期、波速和波形将发生缓慢变化,文中给出了准周期波的周期随深度的变化关系式以及准孤立波波幅、波速随深度的变化关系式,底部水平情形和单层流体情形可看成是本文的特例.Abstract: The nonlinear waves in a stratifiiedfiuid of slowly varying depth are inrestigated in this paper. The model considered here consists of a two-layer incompressible constant-density inviscid fiuid confined by a slightly uneren bottom and a horizontal rigid vrall. The Korteweg-de Vries (KdV) eguation with varving coeffieients is derived with the aid of the reductive perturbation method. By using the method of multiple scales, the upproximate solutions of this eguation are obtained. It is found that the uneve nness of bottom may lead to the generation of so-called quasi-periodic waves quasi-solitary waves, whose periods propugation velocities and wave profiles vary slowly. The relations of the period of guasi-periodic waves and of the amplitude, propagation velocity of quasi-solitary waves varying with the depth of fluid are also presented. The models with two horizontal rigid walls or single-layer fluid can be regarded as particular cases of those in this paper.
-
[1] Yih,C,S.,Stratified flow,Academic Preys,New York(1980). [2] Miles,J,W.,Solitary waves,Ann,Rev,Fluid Mech.,12(1980),11-43. [3] Garrett,C,and W.Munlc,Internal waves in the ocean,Ann,Rev,Fluid Mech.,11(1979),339-369. [4] 戴世强,两层流体界面上的孤立波,应用数学和力学,3,8(1982),721-731. [5] 周显初,缓变的任意截面渠道中的孤立波,应用数学和力学,2(1981),397-906. [6] 周显初,缓变任意截面渠道中的非线性周期波以及孤立波的分裂,中国科学,3,4(1883),238-246. [7] 戴世强,约化摄动法和非线性波远场分析,力学进展,12(1982),2-23. [8] 梅强中(戴世强、周显初整理),《水波动力学》,科学出版社(1984). [9] 刘宇陆,两层流体界面上的二阶椭圆余弦波,上海力学,3(1987),23-28. [10] Apel,J,R.,Satellite sensing of ocean surface dynamics,Ann,Rev,Earth Planet Sci.,8(1980),302-342. [11] Osborne,A,R,and T,L,Burch,Internal solitons in the Andaman sea,Science,208(1980),451-480. -
点击查看大图
计量
- 文章访问数: 1712
- HTML全文浏览量: 73
- PDF下载量: 539
- 被引次数: 0
下载:
