旋涡动力学:从形成、结构到演化

Vortex Dynamics:From Formation,Structure to Evolution

旋涡动力学的核心课题是旋涡结构的形成、演化、稳定性和相互作用。这些过程涉及横场与纵场的非局部耦合,对它们的深入研究是理解各种复杂横场结构,包括湍流相干结构的必要基础。本文以不可压流为例,深入探讨旋涡动力学的几个基础物理理论问题。历史上形成的经典旋涡定义满足不了现代旋涡动力学研究的需要。旋涡并不单纯是涡量场的某种形态,而是高雷诺数下由多种机制有机结合而自然形成的一种流动结构。这种流动经常搓出很薄的剪切层。它一旦处于自由状态,就会迅速地自发卷绕成峰值更强的轴状旋涡,后者成为流体运动包括湍流的肌腱。卷绕的剪切层和轴状涡共处于被称为旋涡的有旋流动结构之中,是高雷诺(Reynolds)数流动的一种基本存在形式。现在,用解析方法研究的旋涡结构及其稳定性的理论已趋于饱和,还满足不了复杂流动包括湍流研究的需要。在业已能够逐步获得复杂流动的数值解和实验解的今天,建立理论—计算—实验的紧密联盟,用一般理论判明旋涡结构的特征量,并用流场数据诊断这些特征量的演化,是值得重视的方向。速度梯度张量的正规-幂零分解为这种理论提供了一个新的局部运动学框架。它既能刻画轴状涡,又能刻画剪切层;既能辨识体元的常规旋转,又能辨识线元的特异旋转;还能揭示每种旋转的不同物理组分及其相互耦合。初步算例表明,应用流场数据考察这些特征量的整体性质、物质演化及其稳定性特征,有望把涡动力学理论研究,特别是湍流涡结构的研究,逐步推进到能够追究过程因果性的崭新阶段。

The central subject of vortex dynamics is the formation,evolution,stability and interaction of vortical structures.These processes involve the nonlocal coupling of longitudinal and transverse field,and their in-depth study is an essential foundation for understanding various complex transverse-field structures,including turbulent coherent structures.This paper takes incompressible flow as an example to discuss in-depth several basic physical theoretical problems of vortex dynamics.The classical definition of vortices based on vorticity tubes or vorticity field cannot meet the needs of modern vortex dynamics studies.A vortex is not simply a certain form of the vorticity field,but a flow structure naturally formed from the inherent combination of various mechanisms at high Reynolds numbers.This flow often creates a thin shear layer.Once free,a shear layer quickly and spontaneously rolls up to an axial vortex of strong peak vorticity,appearing as the sinews and muscles of fluid motion including turbulence.Winding shear layers and axial vortices coexist in a swirling flow structure called a vortex,which is a basic form of flow at high Reynolds numbers.At present,the theory of vortical structure and its stability by analytical method has become nearly saturated but yet cannot meet the needs for studying complex flows including turbulence.Now that numerical and experimental solutions of complex flows can be obtained gradually,it is important to establish a close alliance of theory,computation and experiment,to define the characteristic quantities of vortical structure with general theory,and to diagnose the evolution of these quantities with flow field data.The normalnilpotent decomposition of the velocity gradient tensor provides a perfect local kinematic framework for this kind of theories.It can depict both axial vortex and shear layer.It can identify both normal rotation of volume element and specific rotation of line element.It also reveals the different physical components of each rotation and their coupling.Preliminary case studies indicate that the investigation of the global properties,material evolution and stability of these characteristic quantities with flow data may help advance the theoretical study of vortex dynamics,especially that of turbulent vortical structure,to a new stage where the process causality can be identified.