Introduction to Hydrodynamic Stability

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Cambridge University Press, Sep 9, 2002 - Mathematics - 258 pages
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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 differntial equations, complex variable and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
  

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Contents

General Introduction
1
12 The Methods of Hydrodynamic Stability
6
13 Further Reading and Looking
8
Introduction to the Theory of Steady Flows Their Bifurcations and Instability
10
22 Instability
19
23 Stability and the Linearized Problem
28
KelvinHelmholtz Instability
45
33 Governing Equations for Perturbations
47
72 Instability of Couette Flow
125
73 Gortler Instability
130
Stability of Parallel Flows
138
82 General Properties of Rayleighs Stability Problem
144
83 Stability Characteristics of Some Flows of an Inviscid Fluid
149
84 Nonlinear Perturbations of a Parallel Flow of an Inviscid Fluid
154
Viscous Fluid
156
86 Some General Properties of the OrrSommerfeld Problem
160

34 The Linearized Problem
48
35 Surface Gravity Waves
50
37 RayleighTaylor Instability
51
38 Instability Due to Shear
52
Capillary Instability of a Jet
62
Development of Instabilities in Time and Space
68
52 Weakly Nonlinear Theory
74
53 The Equation of the Perturbation Energy
82
RayleighBenard Convection
93
62 The Linearized Problem
95
63 The Stability Characteristics
97
64 Nonlinear Convection
100
Centrifugal Instability
123
87 Stability Characteristics of Some Flows of a Viscous Fluid
167
88 Numerical Methods of Solving the OrrSommerfeld Problem
171
89 Experimental Results and Nonlinear Instability
172
810 Stability of Axisymmetric Parallel Flows
178
Routes to Chaos and Turbulence
208
92 Routes to Chaos and Turbulence
211
Case Studies in Transition to Turbulence
215
102 Transition of Flow of a Uniform Stream Past a Bluff Body
219
103 Transition of Flows in a Diverging Channel
225
References
237
Index
249
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About the author (2002)

Norman Riley is an Emeritus Professor of Applied Mathematics at the University of East Anglia.

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