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Hydrodynamic instabilities /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Francés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2011.
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| Colección: | Cambridge texts in applied mathematics ;
37. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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).
- 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.
- 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.