湍流是什么？（5）先贤大牛们是如何定义湍流的

由于湍流的极端复杂性质和对它的不完全理解，目前还没有一个公认的湍流定义，以下是流体研究者对湍流的理解，从时间轴上看，对湍流的理解逐渐变得更为深入。

水通过障碍后下落,by达芬奇

列奥纳多·达芬奇在约500年前开创了流体可视化流派，他可能是世界上第一次使用可视化图像作为科学工具来研究湍流的学者。他对湍流的描述如下：

Observe the motion of the surface of the water, which resembles that of hair, 口碑营销公司which has two motions, of whi五证ch one is caused by the weight of the hair, the other by the direction of the curls; thus, the water hasnba历届总冠军 eddying motions, one part of which is due to the pr中科院半导体所incipal currentneccs, the other to the random and reverse motion.

观察水面的运动，它类似于头发，有两种运动，一种是由头发的重量引起的，另一种是由卷发的方向引起的；因此，水有漩涡运动，一部分是由于主流，另一部分是由于随机和反向运动。

达芬奇（约1500）对科马内奇湍流非水镜八奇常着迷，在观察水流时，他给出了可能是湍流的最早定义之一：

the smallest eddies are almost numberless, and large things are rotated only by large eddies and not by small ones and small things are turned by small eddies and large.

最小的涡流几乎数不胜数，大的东西只能被大的涡流而不是小的涡流旋转，小的东西又被小的涡流和大的旋转。

Richardson （192美国民兵2）

“Big whorls have little whorls,which feed on their velocity;And little whorls have lesser whorls,育才学院And so on to viscosit比价神器y”L. F. Richardson. “Weather Prediction by Num超威电池官网erical Process”. Cambridge University Press, 192物料管理2.

大漩涡有小漩涡，以其速度为动力；小漩涡又有更小的漩涡，依此类推直到粘度。

G. I. Taylor（1937）：

“Turbulence is an irregular motion which in general makes its appearance in fluids, gaseous or liquid, when they flow past solid surfaces or even when neighboring streams same fluid past or over one another.”T. Von Karman. “Some remarks on the statistical theory of turbulence”. Proc. 5th Int. Congr. Appl. Mech, Cambridge, MA, 347, 1938

湍流是一种不规则的运动，通常出现在流体中，无论是气态的还是液态的，当它们流过固体表面时，甚至当相邻的流体流过或越过另一流体时。

J. O. Hinze.(1959)

“Turbulent fluid motion is an irregular condition of the flow in which quantities show a random variation with time and space coordinates, so that statistically distinct av中国战争电影erage values can be discerned.“Turbulence”. McGraw-Hill, New York, 1959.

湍流运动是一种不规则的流动状态，在这种状北京广播学院态下，它的物理量随时间和空间坐标的变化而随机变化，因此可以辨别出统计上不同的平均值。

Monin and Yaglom（1971）

“turbulent” flows in which the velocity, pressure, temperature and other fluid mechanical quantities fluctuate in a 企业法律顾问disordered manner with extremely sharp and irregular space- and time-variations.”A. S. Monin and A. M. Yaglom. Statistical Fluid Mechanics: The Mechanics of T什么是债券urbulence, volume 1. M. I. T. Press, 1971.

“湍流"是指速度、压力、温度和其他流体力学量以一种无序的方式，并以极其剧烈和不规则的时空变化而波动的流动。

G. T. Chapman and M. Tobak （1985）,

“Turbulence is any chaotic solution to the 3D Navier–Stokes equations tha面部去皱方法t is sensitive to initial data and which occur柔性电缆s as a result of successive instabilities of laminar flows”G. T. Chapman and M. Tobak. “Observations, Theoret计算机科学概论ical Ideas, and Modeling of Turbulent Flows — Past, Present and Future, in Theoretical Approaches to Turbulence”. Dwoyeret al.(eds), Springer-Verlag, New York, pp. 19–49, 1985.

湍流是对初始数据敏感的三维Navier-Stokes方程的混沌解，它是层流连续不稳定的结果。

S. Rodriguez（2019）

“Turbulent flows is the dynamic superposition of an extremely large number of eddies with random (irregular) but continuous spectrum of sizes and velocities that are interspersed with small, discrete pockets of laminar flow . ”S. Rodriguez. “Applied Computational Fluid Dynamics and Turbulence modeling”. Springer, 2019.

“湍流是大量随机涡流的手枪户型动态叠加(不规则的)，但连续的尺寸和速度谱被层流的小的、离散的群体所分散。