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Cambridge Texts in Applied Mathematics : Introduction to Hydrodynamic Stability Series Number 32 - P. G. Drazin

Cambridge Texts in Applied Mathematics

Introduction to Hydrodynamic Stability Series Number 32


Published: 11th December 2002
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Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

'There is not much to say about this book - if you want to know about hydrodynamic stability, get it, pen and paper, maybe a computer, and start working through it. There is no better way ... Anyone who has worked conscientiously through this book will have no trouble moving on to research in this topic.' The Mathematical Gazette 'Drazin's book is an excellent first introduction to this subject ... and a very useful book has been produced that will be of interest to engineers, physicists and mathematicians starting research in fluid mechanics for many years to come.' The Journal of Fluid Mechanics '... introduces prospective students into its subject at a graduate level. Without either undue oversimplification or oversophistication the author manages to present the fundamentals of hydrodynamic stability in a very lucid way.' Monatshefte fur Mathematik 'Without either undue oversimplification or over-sophistication the author manages to present the fundamentals of hydrodynamic stability in a very lucid way. The exercises constitute a part of particular value. With their many comments and further thoughts they amount to much more than just to exercises in the plain meaning of the word.' Internationale Mathematische Nachrichten

Prefacep. xv
General Introductionp. 1
Preludep. 1
The Methods of Hydrodynamic Stabilityp. 6
Further Reading and Lookingp. 8
Introduction to the Theory of Steady Flows, Their Bifurcations and Instabilityp. 10
Bifurcationp. 10
Instabilityp. 19
Stability and the Linearized Problemp. 28
Kelvin-Helmholtz Instabilityp. 45
Basic Flowp. 45
Physical Description of the Instabilityp. 45
Governing Equations for Perturbationsp. 47
The Linearized Problemp. 48
Surface Gravity Wavesp. 50
Internal Gravity Wavesp. 50
Rayleigh-Taylor Instabilityp. 51
Instability Due to Shearp. 52
Capillary Instability of a Jetp. 62
Rayleigh's Theory of Capillary Instability of a Liquid Jetp. 62
Development of Instabilities in Time and Spacep. 68
The Development of Perturbations in Space and Timep. 68
Weakly Nonlinear Theoryp. 74
The Equation of the Perturbation Energyp. 82
Rayleigh-Benard Convectionp. 93
Thermal Convectionp. 93
The Linearized Problemp. 95
The Stability Characteristicsp. 97
Nonlinear Convectionp. 100
Centrifugal Instabilityp. 123
Swirling Flowsp. 123
Instability of Couette Flowp. 125
Gortler Instabilityp. 130
Stability of Parallel Flowsp. 138
Inviscid Fluidp. 138
Stability of Plane Parallel Flows of an Inviscid Fluidp. 138
General Properties of Rayleigh's Stability Problemp. 144
Stability Characteristics of Some Flows of an Inviscid Fluidp. 149
Nonlinear Perturbations of a Parallel Flow of an Inviscid Fluidp. 154
Viscous Fluidp. 156
Stability of Plane Parallel Flows of a Viscous Fluidp. 156
Some General Properties of the Orr-Sommerfeld Problemp. 160
Energyp. 161
Instability in the inviscid limitp. 163
Stability Characteristics of Some Flows of a Viscous Fluidp. 167
Numerical Methods of Solving the Orr-Sommerfeld Problemp. 171
Experimental Results and Nonlinear Instabilityp. 172
Stability of Axisymmetric Parallel Flowsp. 178
Routes to Chaos and Turbulencep. 208
Evolution of Flows as the Reynolds Number Increasesp. 208
Routes to Chaos and Turbulencep. 211
Case Studies in Transition to Turbulencep. 215
Synthesisp. 215
Introductionp. 215
Instability of flow past a flat plate at zero incidencep. 216
Transition of Flow of a Uniform Stream Past a Bluff Bodyp. 219
Flow past a circular cylinderp. 219
Flow past a spherep. 224
Transition of Flows in a Diverging Channelp. 225
Introductionp. 225
Asymptotic methodsp. 226
Some paradoxesp. 231
Nonlinear wavesp. 232
Conclusionsp. 233
Referencesp. 237
Indexp. 249
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521009652
ISBN-10: 0521009650
Series: Cambridge Texts in Applied Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 278
Published: 11th December 2002
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.5 x 15.1  x 1.4
Weight (kg): 0.38