Ten Chapters in Turbulence: Structure and Dynamics of Vorticity in Turbulence
Ten Chapters in Turbulence: Structure and Dynamics of Vorticity in Turbulence
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湍流十章：湍流中涡度的结构和动力学
DOI：
10.1017/cbo9781139032810.003
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
K. Horiuti
中科院分区：
文献类型：
--
作者：
J. Schumacher;Robert McDougall Kerr;K. Horiuti
介绍古代的流体，可以追溯到米诺斯，设想波和流动的溪流。他们忽略了我们所说的漩涡和湍流。第一位描绘流体的旋转特性、旋涡运动和湍流的艺术家是达芬奇（1506年至1510年）。他会认识到术语涡旋运动，因为它来自拉丁文vortere或vertere：转向，意思是涡旋是气体或液体快速旋转或螺旋的地方。在数学上，人们将这种效应表示为速度导数的扭曲，即速度梯度张量的旋度或反对称分量。如果速度场是u，那么涡量是ω = ω × u。本章将重点讨论的湍流方面是理想化湍流中涡量的结构、动力学和演化--理想化湍流可以是强迫、周期性模拟中均匀、各向同性、统计定常状态的产物，也可以是使用理想化初始条件的流动，这些初始条件旨在让我们理解这些状态。各向同性状态通常被看作是涡量的缠结（至少当振幅很大时是这样），图2.1给出了一个例子。该可视化显示了涡量的等值面，并且之前已经讨论了类似的技术（例如，参见Pullin和Saffman，1998; Ishihara等人，2009; Tsinober，2009）。本章的目标是将这些图形与涡量和应变之间的基本关系联系起来，以及这个学科如何发展到使用涡量作为规律性的度量，然后在考虑理论解释之前，重点讨论湍流中涡量的结构和动力学，实验和数值研究。我们将集中讨论三维湍流。
Introduction Ancient depictions of fluids, going back to the Minoans, envisaged waves and moving streams. They missed what we would call vortices and turbulence. The first artist to depict the rotational properties of fluids, vortical motion and turbulent flows was da Vinci (1506 to 1510). He would recognize the term vortical motion as it comes from the Latin vortere or vertere: to turn, meaning that vorticity is where a gas or liquid is rapidly turning or spiraling. Mathematically, one represents this effect as twists in the velocity derivative, that is the curl or the anti-symmetric component of the velocity gradient tensor. If the velocity field is u , then for the vorticity is ω = ∇ × u . The aspect of turbulence which this chapter will focus upon is the structure, dynamics and evolution of vorticity in idealized turbulence – either the products of homogeneous, isotropic, statistically stationary states in forced, periodic simulations, or flows using idealized initial conditions designed to let us understand those states. The isotropic state is often viewed as a tangle of vorticity (at least when the amplitudes are large), an example of which is given in Fig. 2.1. This visualization shows isosurfaces of the magnitude of the vorticity, and similar techniques have been discussed before (see e.g. Pullin and Saffman, 1998; Ishihara et al., 2009; Tsinober, 2009). The goal of this chapter is to relate these graphics to basic relations between the vorticity and strain, to how this subject has evolved to using vorticity as a measure of regularity, then focus on the structure and dynamics of vorticity in turbulence, in experiments and numerical investigations, before considering theoretical explanations. Our discussions will focus upon three-dimensional turbulence.