对流-扩散相互作用结构的不变性  

INVARIANCE OF INTERACTIVE-STRUCTURE BETWEEN CONVECTION AND DIFFUSION

作　　者：高智[1] 

机构地区：[1]中国科学院力学研究所,北京100080

出　　处：《力学学报》1992年第6期661-670,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金

摘　　要：本文提出并证明了不可压缩剪切层流中对流-扩散相互作用结构不变性诸定理:即二难剪切层流与其线性化及非线性扰动存在同一的对流-扩散相互作用结构,且物理尺度(指时间、空间和速度尺度)相同。给出十个推论,例如:对流-扩散相互作用可在剪切层流及其扰动场内“激发“快时间尺度和小空间尺度结构,线性化稳定性原理的约定对剪切流体系统成立等。应用题例导出计及时间-空间尺度效应和非平行流效应的广义Orr-Sommerfeld(GOS)方程,证实它有两个粘性解:阻尼层解和干扰层解;经典OS方程及其两个粘性解:边界层解和Heisenberg临界层解,Triple-deck稳定性理论基本方程及其两个粘性解,均是本文GOS方程及其两个粘性解的特例。In this paper three invariant theorems of interactive-structure between convection and diffusion for incompressible laminar shear flow and its ten inferences are presented. The invariance of interactive-structure means that the laminar shear flow and its linearized and nonlinear disturbance fields have the same interactive-structure between convection and diffusion and the same physical scales (including the time, spatial and velocity scales). In illustration of the present theoretical application, we derive a generalized Orr-Sommerfeld (GOS) equation, which takes both non-parallel flow effect as well as time-spatial scale effect into account, and find that GOS equation has two viscous solutions corresponding to the retarded layer and the interaction layer, respectively. Special cases of GOS equation with its two viscous solutions include the classical Orr-Sommerfeld equation and the basic equation of Triple-deck stability theory.

关 键 词：粘性流动 剪切流动 对流 扩散 

分 类 号：O357[理学—流体力学]