课程大纲
COURSE SYLLABUS
1.
课程代码/名称
Course Code/Title
MAE5026 海外专家讲学
Lectures from Oversea Experts
2.
课程性质
Compulsory/Elective
选修、Elective
3.
课程学分/学时
Course Credit/Hours
1 学分 / 16 学时
4.
授课语言
Teaching Language
英语
5.
授课教师
Instructor(s)
Luca Biferale
6.
先修要求
Pre-requisites
无
7.
教学目标
Course Objectives
The course is meant to introduce students to open problems to understand basic properties of
turbulent flows for both Eulerian and Lagrangian descriptions, with focus on large- and small-scale
statistics, deviations from Gaussian behavior, direct and inverse cascades. Finally, we shortly present
a couple of applications to Helical and Rotating flows in finite or infinite volumes.
本课程旨在向学生介绍欧拉和拉格朗日描述的湍流中的开放性问题，重点是不同尺度的统计特
性，直接和反向级联。最后，我们简要介绍有限或无限体积中的螺旋和旋转流动的几个应用。
8.
教学方法
Teaching Methods
板书+PPT
9.
教学内容
Course Contents
Section 1
Introduction to statistical description of Turbulent flows: real space,
Fourier space and scale-filtered representation.
Section 2
Introduction to statistical description of Turbulent flows: ergodicity,
definitions of spectra, flux and high order statistics (Flatness, Skewness)
Section 3
Multi-scale statistics: non-Gaussian statistics, intermittency, sub-grid
energy flux, multifractal phenomenology (Eulerian)
Section 4
Lagrangian turbulence: tracers, inertial particles, self-propelling particles.
Preferential concentration and temporal statistical properties.
Section 5
Homogeneous and Isotropic flows: state of the art in 3d. Direct energy
cascade. K41 Theory and corrections to it.
Section 6
Homogeneous and Isotropic flows: state of the art in 2d. Inverse energy
cascade and direct enstrophy cascade. Kraichnan-Batchelor theory.
Section 7
Helical properties in 3d flows. Eulerian and Lagrangian (helicoids).
Section 8
Effects of Rotation: transition from direct to split energy cascades.
10.
课程考核
Course Assessment
请再此注明：①考查/考试；②分数构成。
考察；出勤+报告
11.
教材及其它参考资料
Textbook and Supplementary Readings
[1] U. Frisch. Turbulence (Cambridge University Press, 1995)
[2] S.B. Pope. Turbulent Flows (Cambridge University Press, 2000)
[3]
A. Alexakis and L. Biferale. Cascades and transitions in turbulent flows. Phys. Rep. 2018
https://doi.org/10.1016/j.physrep.2018.08.001 arXiv:1808.06186
[4] F. Toschi and E. Bodenschatz. Lagrangian Properties of Particles in Turbulence. Annu. Rev. Fluid
Mech. 41, 375 (2009)
