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Introduction to Hydrodynamic Stability / Edition 1
     

Introduction to Hydrodynamic Stability / Edition 1

by P. G. Drazin
 

ISBN-10: 0521009650

ISBN-13: 9780521009652

Pub. Date: 09/28/2002

Publisher: Cambridge University Press

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment. They are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography, physics, and engineering. This is a graduate-level textbook to introduce these phenomena by modeling them mathematically, and describing

Overview

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment. They are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography, physics, and engineering. This is a graduate-level textbook to introduce these phenomena by modeling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized with many figures. 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 is very useful for specialists in other fields.

Product Details

ISBN-13:
9780521009652
Publisher:
Cambridge University Press
Publication date:
09/28/2002
Series:
Cambridge Texts in Applied Mathematics Series , #32
Edition description:
New Edition
Pages:
276
Product dimensions:
5.98(w) x 8.98(h) x 0.67(d)

Table of Contents

Prefacexv
1General Introduction1
1.1Prelude1
1.2The Methods of Hydrodynamic Stability6
1.3Further Reading and Looking8
2Introduction to the Theory of Steady Flows, Their Bifurcations and Instability10
2.1Bifurcation10
2.2Instability19
2.3Stability and the Linearized Problem28
3Kelvin-Helmholtz Instability45
3.1Basic Flow45
3.2Physical Description of the Instability45
3.3Governing Equations for Perturbations47
3.4The Linearized Problem48
3.5Surface Gravity Waves50
3.6Internal Gravity Waves50
3.7Rayleigh-Taylor Instability51
3.8Instability Due to Shear52
4Capillary Instability of a Jet62
4.1Rayleigh's Theory of Capillary Instability of a Liquid Jet62
5Development of Instabilities in Time and Space68
5.1The Development of Perturbations in Space and Time68
5.2Weakly Nonlinear Theory74
5.3The Equation of the Perturbation Energy82
6Rayleigh-Benard Convection93
6.1Thermal Convection93
6.2The Linearized Problem95
6.3The Stability Characteristics97
6.4Nonlinear Convection100
7Centrifugal Instability123
7.1Swirling Flows123
7.2Instability of Couette Flow125
7.3Gortler Instability130
8Stability of Parallel Flows138
Part 1Inviscid Fluid138
8.1Stability of Plane Parallel Flows of an Inviscid Fluid138
8.2General Properties of Rayleigh's Stability Problem144
8.3Stability Characteristics of Some Flows of an Inviscid Fluid149
8.4Nonlinear Perturbations of a Parallel Flow of an Inviscid Fluid154
Part 2Viscous Fluid156
8.5Stability of Plane Parallel Flows of a Viscous Fluid156
8.6Some General Properties of the Orr-Sommerfeld Problem160
8.6.1Energy161
8.6.2Instability in the inviscid limit163
8.7Stability Characteristics of Some Flows of a Viscous Fluid167
8.8Numerical Methods of Solving the Orr-Sommerfeld Problem171
8.9Experimental Results and Nonlinear Instability172
8.10Stability of Axisymmetric Parallel Flows178
9Routes to Chaos and Turbulence208
9.1Evolution of Flows as the Reynolds Number Increases208
9.2Routes to Chaos and Turbulence211
10Case Studies in Transition to Turbulence215
10.1Synthesis215
10.1.1Introduction215
10.1.2Instability of flow past a flat plate at zero incidence216
10.2Transition of Flow of a Uniform Stream Past a Bluff Body219
10.2.1Flow past a circular cylinder219
10.2.2Flow past a sphere224
10.3Transition of Flows in a Diverging Channel225
10.3.1Introduction225
10.3.2Asymptotic methods226
10.3.3Some paradoxes231
10.3.4Nonlinear waves232
10.3.5Conclusions233
References237
Index249

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