课程大纲
COURSE SYLLABUS
1.
课程代码/名称
Course Code/Title
MAE5015
湍流
Turbulent Flows
2.
课程性质
Compulsory/Elective
专业选修课
Subject-Elective
3.
课程学分/学时
Course Credit/Hours
3
学分
/ 48
学时
3 Credits / 48 Hours
4.
授课语言
Teaching Language
英文
English
5.
授课教师 Instructor(s)
夏克青
XIA Ke-qing
6.
先修要求
Pre-requisites
掌握基本的流体力学知识
Fluid mechanics background required
7.
教学目标 Course Objectives
湍流是自然界和各种工程应用中普遍存在的流体运动状态，也是非常具有挑战性的物理问
题。本门课程将会介绍湍流的基本概念，例如湍流的时间和空间尺度、雷诺剪切应力、湍
动能和能谱、能量级串等，并将这些知识应用到不同的湍流系统当中，具体包括均匀各向
同性湍流、壁湍流、可压缩湍流和二维湍流。在本课程当中，学生需要阅读相关的经典文
献和最新的研究综述，从而更好地了解湍流研究的现状和未来的发展趋势。
This course is to introduce the phenomena and theory of turbulence, a very common state of fluid
motion in nature and engineering, and a very challenging physical problem. In this course, we will
introduce a number of fundamental concepts about turbulence, such as the range of scales,
Reynolds stress, the turbulence kinetic energy budget, and energy cascade. We focus on both
understanding the fundamentals and the use of such knowledge in various kinds of turbulent flows.
Specific flow phenomena addressed will include homogeneous isotropic flows, wall-bounded
flows, compressible flows and two dimensional flow. Students will be required to explore classical
and recent literature to study the development of turbulence research.
8.
教学方法 Teaching Methods
讲授
+
习题课
+
课程项目
Lecture + Tutorial + Project
9.
教学内容 Course Contents
绪论（
3
学时）：
湍流的基本特性，湍流的空间和时间尺度，分析湍流问题的基本方法，湍
流研究进展回顾
Introduction (3 hours):
The nature of turbulence, Length and time scales in turbulent flows, Basic
methods for analysis of turbulence, An overview of recent development
流体运动方程（3 学时）：
Navier-Stokes
方程的张量形式，压强的作用，被动标量，涡量方程，流体
的拉伸和旋转，欧拉场和拉格朗日场
The equations of fluid motion (3 hours):
Navier-Stokes equations in tensor form, The role of pressure, Conserved passive
scalars, The vorticity equation, Rates of strain and rotation, Eulerian and
Lagrangian fields
概率描述方法（
3
学时）：
随机变量的特征，耦合随机变量，随机过程，统计取样，概率和平均
The statistical description (3 hours):
Characterization of random variables, Joint random variables, Random processes,
Statistical sampling, Probability and averaging
平均流动方程（
3
学时）：
雷诺方程，雷诺应力，平均标量方程，梯度扩散，湍流粘度假设
Mean-flow equations (3 hours):
Reynolds equations, Reynolds stresses, The mean scalar equation, Gradient-
diffusion, Turbulent-viscosity hypotheses
湍流动能和湍流动力学（3 学时）：
湍动能，湍动能方程，涡动力学
Kinetic energy budget and turbulent dynamics (3 hours):
Kinetic energy, Kinetic energy equation and energy budget, Vortex dynamics
能谱（3 学时）：
相关函数和结构函数，波数空间的能谱，谱传递，傅立叶模态的演化
The spectral descriptions (3 hours):
Correlations and structure functions, Spectra in wave number space, Spectral
transfer, The evolution of Fourier modes
能量级串和相似性（3 学时）：
能量级串，
Kolmogorov
假设，局部各向同性，均匀各向同性湍流，
2/3
律
和 4/5 律，间歇性
Energy cascade and scale similarity (3 hours):
Energy cascade, Kolmogorov’s hypotheses, Local isotropy, Homogeneous
isotropic flow, Inertial range, The two-thirds and four-fifths laws, Intermittency
自由剪切流（3 学时）：
湍流射流、湍流尾流、混合层、热羽流
Free shear flow (3 hours):
Turbulent jets, Turbulent wakes, Mixing layers, Thermal plumes
壁湍流（
3
学时）：
槽道流，管道流，近壁剪切，摩阻律，壁粗糙度，混合长
Wall-bounded shear flows (3 hours):
Channel flow, Pipe flow, The near-wall shear stress, The friction law, Wall
roughness, The mixing length
边界层（3 学时）：
平均速度剖面，内标度和外标度，指数律层，湍流猝发和湍流结构
Boundary Layers (3 hours):
Mean velocity profiles, Inner and outer scalings, Logarithmic layer, Turbulent
bursts and structures
可压缩湍流（3 学时）：
可压缩效应，密度涨落，激波，激波和湍流的相互作用
Compressible turbulence (3 hours):
Effects of compressibiltiy, Density fluctuations, Shock wake, Shock-turbulence
interactions
二维湍流（3 学时）：
二维流动，能量反级串，涡拟能级串
Two dimensional turbulence (3 hours):
Two dimensional flow, Inverse energy cascade, Enstrophy cascade
湍流扩散（3 学时）：
湍流的拉格朗日描述，相对扩散，单粒子扩散，双粒子扩散，Richardson 维
象论
Turbulent Dispersion (3 hours):
Lagrangian characteristics of turbulence, Relative dispersion, Single particle
dispersion, Pair dispersion, Richardson’s phenomenology
湍流研究进展：理论（3 学时）：
Kolmogorov
理论回顾，多分形模型，壳模型，临界现象，重整化群方法
Recent development in turbulence I: Theory (3 hours):
Revisit Kolmogorov theory, Multifractal model, Shell model, Critical
phenomena, Renormalization group method
湍流研究进展：实验（3 学时）：
高雷诺数实验，现代湍流研究中的实验技术和设备
Recent development in turbulence II: Experiment (3 hours):
High Reynolds number experiments, Modern techniques and facilities in
turbulence research
湍流研究进展：模拟和计算方法（3 学时）：
RANS
方法，大涡模拟方法，直接数值模拟
Recent development in turbulence III: Modelling and simulation (3 hours):
Reynolds-averaged Navier-Stokes approaches, Large-eddy simulation, Direct
numerical simulation
10.
课程考核 Course Assessment
课堂表现 10% + 平时作业 20% + 课程项目 30% + 测验 40% (20%×2)
Class Performance 10% + Assignments 20% + Project 30% + Tests 40% (20%
×
2)
11.
教材及其它参考资料 Textbook and Supplementary Readings
教材/Textbook
Turbulent Flows by S.B. Pope (2000, Cambridge University Press).
参考书目/Supplementary readings
1. A First Course in Turbulence by H. Tennekes and J.L. Lumley (1972).
2. Statistical Fluid Mechanics (Vols. 1–2) by A.S. Monin & A.M. Yaglom (1971, 1975).
3. Lectures in Turbulence for the 21st Century by William K. George (2013).
4. A Voyage Through Turbulence edited by P.A. Davidson, Y. Kaneda, K. Moffatt and K.R.
Sreenivasan (2011).
5. An Introduction to Turbulent Flow by J. Mathieu and J. Scott (2000).
6. Turbulence: an Introduction for Scientists and Engineers by P.A. Davidson (2004).
7. Turbulence: the Legacy of A.N. Kolmogorov by U. Frisch (1995).
8. The Physics of Fluid Turbulence by W.D. McComb (1990).