Course Identification

Fluid mechanics
20221101

Lecturers and Teaching Assistants

Prof. Gregory Falkovich
Dr. Michal Shavit

Course Schedule and Location

2022
First Semester
Monday, 11:15 - 13:00, Weissman, Seminar Rm A

Tutorials
Tuesday, 09:15 - 10:00, Weissman, Seminar Rm B
25/10/2021
18/03/2022

Field of Study, Course Type and Credit Points

Physical Sciences: Lecture; Elective; Regular; 3.00 points
Chemical Sciences: Lecture; Elective; Regular; 3.00 points

Comments

N/A

Prerequisites

No

Restrictions

30

Language of Instruction

English

Attendance and participation

Expected and Recommended

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)

100%

Evaluation Type

Examination

Scheduled date 1

03/03/2022
Weissman, Seminar Rm A
0900-1300
N/A

Scheduled date 2

16/03/2022
Weissman, Seminar Rm B
0900-1300
N/A

Estimated Weekly Independent Workload (in hours)

2

Syllabus

Link for this course: http://www.weizmann.ac.il/complex/falkovich/fluid-mechanics 

http://www.weizmann.ac.il/complex/falkovich/sites/weizmann.ac.il.complex.falkovich/files/FluidShort.pdf 

1 Basic equations and steady flows 2

1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Lecture 1 Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Lecture 2 Conservation laws and steady flows . . . . . . . . . . . . . . . 10
1.3.1 Kinematics and Kelvin theorem . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Energy and momentum fluxes . . . . . . . . . . . . . . . . . . . . . . 11
1.3.3 Irrotational and incompressible flows . . . . . . . . . . . . . . . . . . 13
1.3.4 Flow past a rigid body and flow due to a moving body . . . . . . . . 16
1.3.5 Quasi-momentum and induced mass . . . . . . . . . . . . . . . . . . 20

1.4 Lecture 3 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 Reversibility paradox and D'Alembert's paradox . . . . . . . . . . . 23
1.4.2 Viscous stress tensor and the strain tensor . . . . . . . . . . . . . . . 24
1.4.3 Navier-Stokes equation . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.4.4 Law of similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.5 Lecture 4 Stokes flow and wake . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.1 Stokes flow around a sphere . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.2 Boundary layer and wake . . . . . . . . . . . . . . . . . . . . . . . . 31



2 Unsteady flows: Instabilities, Turbulence and Shocks 37

2.1 Lecture 5 Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2 Lecture 6 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.1 Cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.2 Turbulent river and wake . . . . . . . . . . . . . . . . . . . . . . . . 43

2.3 Lecture 7 Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.1 Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.2 Riemann wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.3 Burgers equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.4 Acoustic turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.5 Mach number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53



3 Dispersive Waves 57

3.1 Lecture 8 Linear waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2 Lecture 9 Weakly nonlinear waves . . . . . . . . . . . . . . . . . . . . . 62

3.3 Lecture 10 Nonlinear Schrodinger Equation . . . . . . . . . . . . . . . . . 68
3.3.1 Derivation of NSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3.2 Modulational instability . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3.3 Solitons, collapse and turbulence . . . . . . . . . . . . . . . . . . . . 72

3.4 Lecture 11 Korteveg - de Vries Equation . . . . . . . . . . . . . . . . . . 76

Learning Outcomes

Upon successful completion of this course students should be able to:

  1. Demonstrate knowledge of fluid mechanics, both on a conceptual and a technical level.

Reading List

Website

N/A