二维平行壁面剪切流动的转捩与混沌模型  

The Transitional and chaotic Models of Two-dimensional Parallel Wall Shear Flows

作　　者：杨立[1] 华顺芳[1] 杜先之[1] 

机构地区：[1]海军工程学院热工教研室,武汉430033

出　　处：《水动力学研究与进展（A辑）》1994年第6期724-735,共12页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金

摘　　要：本文利用约化摄动方法,从理论上研究了二维平行壁面剪切流动的转捩与混沌现象,得到了描述二维平行壁面流动中的小振幅T—S波的演化方程为Korteweg—DcVries—Burgers方程,反映T—S波衰减或增长率的参数为KdV—Burgers方程中的耗散系数v_1与色散系数δ的比值v_1/(δ^(1/2)),v_1和δ由流场结构决定的。当T—S波振幅被放大到一定程度后将受到的自由流中的高次或亚谐波的激励,经过分叉而进入混沌状态。二维平行壁面剪切流动进入混沌的现象可用含二次非线性项的强迫振动方程来描述。从周期运动的T—S波进入混沌至少有以下两种途径。一是倍分叉途径;另一种是偶阶次次谐分叉途径。由哪一条途径进入混沌取决于自由流中扰动量的激励频率和流场的耗散系数与色散系数的比值。In this paper, the transitional and chaotic phenomena in the two-dimensional parallel wall shear flows are studied using the two-dimensional reductire perturbation method. The evolution equation describing the T-S wave formed in wall shear flows is obtained. This nonlinear evolution equation is called a Korteweq-de Vries-jBurgers equation. The Grow and damp of T-S wave are determined by the parameter , where vi is called a dissipation coefficient, S is called dispersion coefficients depend the structure of flow field. When the amplitude of T-S wave grows to some extent. It will bifurcate and finall go to chaos excited by the harmonic or subharmonic disturbances in the tree streams. The bifurcation and chaotic process of two-dimensional parallel wall shear flows are described by the forced oscillation equation containing a square nonlinear term. There are two routes from periodic to chaoticmotion for T-S wave. The one is perivd doubing route. The other is even subharmome bifurcation route. From which route to chaos is determined by the exciting frequency of disturbance in free stream and the parameter v1

关 键 词：壁面剪切流 转捩 浑沌 流体动力学 湍流 

分 类 号：O357.52[理学—流体力学]