# The Couette-Taylor Problem

Part of the Applied Mathematical Sciences book series (AMS, volume 102)

1. Front Matter
Pages i-ix
2. Pascal Chossat, Gérard Iooss
Pages 1-11
3. Pascal Chossat, Gérard Iooss
Pages 13-33
4. Pascal Chossat, Gérard Iooss
Pages 35-58
5. Pascal Chossat, Gérard Iooss
Pages 59-104
6. Pascal Chossat, Gérard Iooss
Pages 105-132
7. Pascal Chossat, Gérard Iooss
Pages 133-165
8. Pascal Chossat, Gérard Iooss
Pages 167-205
9. Pascal Chossat, Gérard Iooss
Pages 207-219
10. Back Matter
Pages 221-234

### Introduction

1. 1 A paradigm About one hundred years ago, Maurice Couette, a French physicist, de­ signed an apparatus consisting of two coaxial cylinders, the space between the cylinders being filled with a viscous fluid and the outer cylinder being rotated at angular velocity O2. The purpose of this experiment was, follow­ ing an idea of the Austrian physicist Max Margules, to deduce the viscosity of the fluid from measurements of the torque exerted by the fluid on the inner cylinder (the fluid is assumed to adhere to the walls of the cylinders). At least when O is not too large, the fluid flow is nearly laminar and 2 the method of Couette is valuable because the torque is then proportional to 110 , where II is the kinematic viscosity of the fluid. If, however, O is 2 2 increased to a very large value, the flow becomes eventually turbulent. A few years later, Arnulph Mallock designed a similar apparatus but allowed the inner cylinder to rotate with angular velocity 01, while O2 = o. The surprise was that the laminar flow, now known as the Couette flow, was not observable when 0 exceeded a certain "low" critical value Ole, even 1 though, as we shall see in Chapter II, it is a solution of the model equations for any values of 0 and O .

### Keywords

Finite Invariant Manifold Navier-Stokes equation average differential equation equation fluid mechanics function geometry partial differential equation stability theorem vortices waves

#### Authors and affiliations

1. 1.Institut Non Linéaire de NiceUMR 129 CNRS-UNSAValbonneFrance

### Bibliographic information

• Book Title The Couette-Taylor Problem
• Authors Pascal Chossat
Gerard Iooss
• Series Title Applied Mathematical Sciences
• DOI https://doi.org/10.1007/978-1-4612-4300-7
• Copyright Information Springer-Verlag New York 1994
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-94154-7
• Softcover ISBN 978-1-4612-8730-8
• eBook ISBN 978-1-4612-4300-7
• Series ISSN 0066-5452
• Edition Number 1
• Number of Pages X, 234
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site