Introduction to Hydrodynamic Stability

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Paperback | 11 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.

Industry Reviews

'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

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Non-Fiction Science Physics Classical Mathematics Fluid Mechanics Wave Mechanics including Vibration & Acoustics Mathematics Applied Mathematics

Preface	p. xv
General Introduction	p. 1
Prelude	p. 1
The Methods of Hydrodynamic Stability	p. 6
Further Reading and Looking	p. 8
Introduction to the Theory of Steady Flows, Their Bifurcations and Instability	p. 10
Bifurcation	p. 10
Instability	p. 19
Stability and the Linearized Problem	p. 28
Kelvin-Helmholtz Instability	p. 45
Basic Flow	p. 45
Physical Description of the Instability	p. 45
Governing Equations for Perturbations	p. 47
The Linearized Problem	p. 48
Surface Gravity Waves	p. 50
Internal Gravity Waves	p. 50
Rayleigh-Taylor Instability	p. 51
Instability Due to Shear	p. 52
Capillary Instability of a Jet	p. 62
Rayleigh's Theory of Capillary Instability of a Liquid Jet	p. 62
Development of Instabilities in Time and Space	p. 68
The Development of Perturbations in Space and Time	p. 68
Weakly Nonlinear Theory	p. 74
The Equation of the Perturbation Energy	p. 82
Rayleigh-Benard Convection	p. 93
Thermal Convection	p. 93
The Linearized Problem	p. 95
The Stability Characteristics	p. 97
Nonlinear Convection	p. 100
Centrifugal Instability	p. 123
Swirling Flows	p. 123
Instability of Couette Flow	p. 125
Gortler Instability	p. 130
Stability of Parallel Flows	p. 138
Inviscid Fluid	p. 138
Stability of Plane Parallel Flows of an Inviscid Fluid	p. 138
General Properties of Rayleigh's Stability Problem	p. 144
Stability Characteristics of Some Flows of an Inviscid Fluid	p. 149
Nonlinear Perturbations of a Parallel Flow of an Inviscid Fluid	p. 154
Viscous Fluid	p. 156
Stability of Plane Parallel Flows of a Viscous Fluid	p. 156
Some General Properties of the Orr-Sommerfeld Problem	p. 160
Energy	p. 161
Instability in the inviscid limit	p. 163
Stability Characteristics of Some Flows of a Viscous Fluid	p. 167
Numerical Methods of Solving the Orr-Sommerfeld Problem	p. 171
Experimental Results and Nonlinear Instability	p. 172
Stability of Axisymmetric Parallel Flows	p. 178
Routes to Chaos and Turbulence	p. 208
Evolution of Flows as the Reynolds Number Increases	p. 208
Routes to Chaos and Turbulence	p. 211
Case Studies in Transition to Turbulence	p. 215
Synthesis	p. 215
Introduction	p. 215
Instability of flow past a flat plate at zero incidence	p. 216
Transition of Flow of a Uniform Stream Past a Bluff Body	p. 219
Flow past a circular cylinder	p. 219
Flow past a sphere	p. 224
Transition of Flows in a Diverging Channel	p. 225
Introduction	p. 225
Asymptotic methods	p. 226
Some paradoxes	p. 231
Nonlinear waves	p. 232
Conclusions	p. 233
References	p. 237
Index	p. 249
Table of Contents provided by Syndetics. All Rights Reserved.

Introduction to Hydrodynamic Stability

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