| Description |
1 online resource (xviii, 391 pages) : illustrations |
| Series |
Cambridge texts in applied mathematics ; [37] |
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Cambridge texts in applied mathematics ; 37.
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| Contents |
Cover; Title; Copyright; Contents; Foreword; Preface; Video resources; 1 Introduction; 1.1 Phase space, phase portrait; 1.2 Stability of a fixed point; 1.2.1 Fixed points; 1.2.2 Linear stability of a fixed point; 1.2.3 Stability of a nonhyperbolic fixed point; 1.3 Bifurcations; 1.3.1 Definition; 1.3.2 Saddle -- node bifurcation; 1.3.3 Pitchfork bifurcation; 1.3.4 Hopf bifurcation; 1.4 Examples from hydrodynamics; 1.4.1 Stability of a soap film; 1.4.2 Stability of a bubble; 1.4.3 Stability of a colloidal suspension; 1.4.4 Convection in a ring; 1.4.5 Double diffusion of heat and matter |
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1.5 Non-normality of the linearized operator1.5.1 Algebraic transient growth; 1.5.2 Optimal excitation of an unstable mode; 1.6 Exercises; 1.6.1 The forced harmonic oscillator; 1.6.2 Particle in a double-well potential; 1.6.3 Avalanches in a sand pile; 1.6.4 A second-order phase transition; 1.6.5 A first-order phase transition; 1.6.6 A model of soap-film instability; 1.6.7 Transient growth and optimal perturbation; 1.6.8 Optimal excitation of an unstable mode; 1.6.9 Subcritical bifurcation via a transient growth; 2 Instabilities of fluids at rest; 2.1 Introduction |
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2.2 The Jeans gravitational instability2.2.1 Acoustic waves; 2.2.2 The effect of gravity at large scales; 2.2.3 Discussion; 2.3 The Rayleigh -- Taylor interface instability; 2.3.1 Dimensional analysis; 2.3.2 Perturbation equations; 2.3.3 Linearization, normal modes, and the dispersion relation; 2.3.4 Discussion; 2.3.5 The effects of horizontal walls and viscosity; 2.4 The Rayleigh -- Plateau capillary instability; 2.4.1 Description; 2.4.2 Dimensional analysis; 2.5 The Rayleigh -- Bénard thermal instability; 2.5.1 Description; 2.5.2 The instability mechanism (Pr 1) |
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2.5.3 Study of stability within the Boussinesq approximation2.6 The Bénard -- Marangoni thermocapillary instability; 2.6.1 Description; 2.6.2 Dimensional analysis; 2.7 Discussion; 2.7.1 Characteristic scales and mode selection; 2.7.2 General characteristics of a threshold instability; 2.8 Exercises; 2.8.1 Rayleigh -- Taylor instability between walls; 2.8.2 Instability of a suspended thin film; 2.8.3 Rayleigh -- Plateau instability on a wire; 2.8.4 Stability of a planar front between two fluids in a porous medium; 2.8.5 The Darrieus -- Landau instability of a flame front |
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3 Stability of open flows: basic ideas3.1 Introduction; 3.1.1 Linear dynamics of a wave packet; 3.1.2 Stability in the Lyapunov sense, asymptotic stability; 3.1.3 Linear stability and instability; 3.2 A criterion for linear stability; 3.2.1 Spatio-temporal evolution of a general perturbation; 3.2.2 An illustration; 3.3 Convective and absolute instabilities; 3.3.1 The criterion for absolute instability; 3.3.2 The spatial branches of a convective instability; 3.3.3 Illustrations; 3.3.4 The Gaster relation; 3.4 Exercises; 3.4.1 Dispersion of a wave packet |
| Summary |
"The instability of fluids is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics and meteorology. This modern introduction is written for any student, researcher or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamics provides the basic structure of the exposition and, wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. Asymptotic methods also play an important role. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Unsteady flow (Fluid dynamics)
|
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TECHNOLOGY & ENGINEERING -- Material Science.
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Unsteady flow (Fluid dynamics)
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| Form |
Electronic book
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| ISBN |
9781139127691 |
|
1139127691 |
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9780511975172 |
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0511975171 |
|
9781139114868 |
|
1139114867 |
|
1139117033 |
|
9781139117036 |
|
1107225329 |
|
9781107225329 |
|
1283295938 |
|
9781283295932 |
|
1139122770 |
|
9781139122771 |
|
9786613295934 |
|
6613295930 |
|
1139112678 |
|
9781139112673 |
|
