Instability

ME-466 / 3 credits

Teacher: Gallaire François

Language: 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

Recommended courses

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

Learning Outcomes

By the end of the course, the student must be able to:

  • Describe the physical differences between laminar and turbulent flows, AH4
  • Implement the basics of computer programming; develop a (simple) structures software using a programming language / environment such as C, Fortran or Matlab, AH40

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, exercices 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.

Assessment methods

Written exam.

Supervision

Office hours Yes
Assistants Yes
Forum No

Resources

Bibliography

Instabilités hyrodynamiques, F. Charru, CNRS Editions, 2007 [in FRENCH]

Hydrodynamic instabilities, F. Charru, Cambrdige Univ. Press, 2011 [in ENGLISH]


Introduction to Hydrodynamic Stability, P.G. Drazin, Cambridge Univ. Press, 2002

 

 

Ressources en bibliothèque

Websites

Moodle Link

In the programs

  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Instability
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 1 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Instability
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 1 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Instability
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 1 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Instability
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 1 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Instability
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 1 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Instability
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 1 Hour(s) per week x 14 weeks
  • Type: optional
  • Exam form: Written (winter session)
  • Subject examined: Instability
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 1 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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