摘要
给出两水平固壁间两层不可压缩理想流体中二维非线性界面波的演化方程.首先建立出这个演化方程,并由此方程在一定条件下得到二维非线性界面长波满足的近似方程.然后从理论上证明这个长波近似方程包含了以下两个描述一阶界面升高的著名的浅水孤立波方程: Korteweg-de Vries(KdV)方程和Kadomtsev-Petviashvili(KP)方程.所得特殊结果与前人的一致,表明所建立的二维非线性界面波演化方程正确且具有一般性.
The simpler models of one-dimensional internal solitary waves in stratified fluid have been studied by many authors. Nevertheless, there seem to be fewer reports on the two-dimensional internal solitary waves, which frequently appear in nature. For more general cases, for example, the propagation and interaction of internal waves in stratified oceans or atmosphere, the two-dimensional model has to be considered. In the present paper, the two-dimensional weakly nonlinear waves at the interface between the two-layer incompressible inviscid fluids bounded by two horizontal rigid walls are investigated. Firstly, the governing equations in a concise form are presented with no a priori assumption about the horizontal length scales or about the direction of propagation by means of small parameter expansion and by introducing the pseudo-differential operators from the boundary value problem of potential flow theory. These equations are similar to those presented by Milewski & Keller[13], if σ = 0. Then the approximate equations for the two-dimensional interfacial long waves are derived by introducing the horizontal length scales, and then, the Korteweg-de Vries (KdV) equation is deduced under the shallow water assumption, and the Kadomtsev-Petviashvili (KP) equation is also derived with the further assumption that a certain propagating direction is preferential. The conclusions in this paper are in good agreement with some classical results, which are considerably extended. It is illustrated that the governing evolution equation given here is correct and of a wide range of validity. We will further investigate the applicable range of the governing equation.
出处
《力学学报》
EI
CSCD
北大核心
2003年第2期213-217,共5页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(19672035)
华北电力大学博士学位教师科研基金资助项目.
