# Coursebooks

## Instability

#### Lecturer(s) :

Gallaire François

English

#### Summary

This course focuses on the physical mechanisms at the origin of the transition of a flow from laminar to turbulent using the hydrodynamic instability theory.

#### Content

Learn to understand the complex phenomena originating in the destabilization of laminar flows, and their transition to turbulence. Know how to linearize the fluid equations and to formulate the question of stability of a flow in terms of an eigenvalue problem and a dispersion relation. Identify the physical mechanisms resulting in classical instabilities as Kelvin-Helmholtz instability. Spatial instability in open flows. Understanding the different types of bifurcations. Reading scientific literature.

#### Keywords

Instability, linearization, bifurcation

#### Learning Prerequisites

##### Required courses

Incompressible fluid mechanics

hydrodynamics

##### Important concepts to start the course

• concept of linear operator and eigenvalues
• be able to solve a linear differential system at constant coefficients
• Fourier analysis
• Taylor expansions
• Navier-Stokes equations
• Use a work methodology appropriate to the task.
• Use both general and domain specific IT resources and tools
• Make an oral presentation.
• Write a literature review which assesses the state of the art.
• Summarize an article or a technical report.

#### Learning Outcomes

By the end of the course, the student must be able to:
• Describe the physical differences between laminar and turbulent flows, AH4
• Integrate the basics of computer programming; develop a (simple) structures software using a programming language / environment such as C, Fortran or Matlab, AH25

#### Transversal skills

• Use both general and domain specific IT resources and tools
• Write a literature review which assesses the state of the art.
• Use a work methodology appropriate to the task.
• Summarize an article or a technical report.

#### Teaching methods

Lectures, exercice and homework

#### Expected student activities

The students should follow the lectures and practise at home both the resolution of application exercises and the reading of scientific articles.

Written exam.

#### Supervision

 Office hours Yes Assistants No Forum No

#### Resources

##### Bibliography

Instabilités hyrodynamiques, F. Charru, CNRS Editions, 2007
Introduction to Hydrodynamic Stability, P.G. Drazin, Cambridge Univ. Press, 2002.

### In the programs

• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Instability
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Instability
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Energy Management and Sustainability, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Instability
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Energy Management and Sustainability, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Instability
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Instability
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Instability
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Semester
Fall
• Exam form
Written
• Credits
3
• Subject examined
Instability
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German