Hydrodynamic Instabilities.
This modern account brings the subject to life by emphasising the physical mechanisms involved. Contains exercises and useful references.
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| Author / Creator: | |
|---|---|
| Other Authors / Creators: | de Forcrand-Millard, Patricia. |
| Format: | eBook Electronic |
| Language: | English |
| Imprint: | Cambridge : Cambridge University Press, 2011. |
| Series: | Cambridge Texts in Applied Mathematics
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| Subjects: | |
| Local Note: | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| Online Access: | Click to View |
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| 100 | 1 | |a Charru, François. | |
| 245 | 1 | 0 | |a Hydrodynamic Instabilities. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2011. | |
| 264 | 4 | |c ©2011. | |
| 300 | |a 1 online resource (412 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge Texts in Applied Mathematics ; |v v.37 | |
| 505 | 0 | |a 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 operator -- 1.5.1 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 instability -- 2.2.1 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). | |
| 505 | 8 | |a 2.5.3 Study of stability within the Boussinesq approximation -- 2.6 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 ideas -- 3.1 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 -- 3.4.2 Spatial branches of a convective instability -- 4 Inviscid instability of parallel flows -- 4.1 Introduction -- 4.2 General results -- 4.2.1 Linearized equations for small perturbations -- 4.2.2 The Squire theorem -- 4.2.3 The Rayleigh equation of two-dimensional perturbations -- 4.2.4 The Rayleigh inflection point theorem -- 4.2.5 Jump conditions between two layers of uniform vorticity -- 4.3 Instability of a mixing layer -- 4.3.1 Kelvin--Helmholtz instability of a vortex sheet -- 4.3.2 The case of nonzero vorticity thickness -- 4.3.3 Viscous effects -- 4.4 The Couette--Taylor centrifugal instability -- 4.4.1 Introduction -- 4.4.2 The steady flow and its instability. | |
| 505 | 8 | |a 4.4.3 The instability criterion for inviscid flow -- 4.4.4 The effect of viscosity: the Taylor number -- 4.5 Exercises -- 4.5.1 The Kelvin--Helmholtz instability with gravity and capillarity -- 4.5.2 The effect of walls on the Kelvin--Helmholtz instability -- 4.5.3 Internal waves in a density-stratified shear flow -- 4.5.4 Instability of inviscid Couette--Taylor flow -- 4.5.5 Instability of a viscous film -- 5 Viscous instability of parallel flows -- 5.1 Introduction -- 5.1.1 Instability of Poiseuille flow in a tube -- 5.1.2 Instability of a boundary layer -- 5.2 General results -- 5.2.1 The linearized perturbation equations -- 5.2.2 The Squire theorem -- 5.2.3 The Orr--Sommerfeld equation -- 5.2.4 The viscous instability mechanism -- 5.3 Plane Poiseuille flow -- 5.3.1 Marginal stability, eigenmodes -- 5.3.2 Experimental study for small perturbations -- 5.3.3 Transient growth -- 5.4 Poiseuille flow in a pipe -- 5.5 Boundary layer on a flat surface -- 5.5.1 Experimental demonstration -- 5.5.2 Local analysis -- 5.5.3 Eigenmodes, marginal stability, and nonparallel effects -- 5.5.4 Transient growth -- 5.6 Exercises -- 5.6.1 A marginal curve -- 5.6.2 Solution of the Orr--Sommerfeld equation for plug flow -- 5.6.3 Solution of the Orr--Sommerfeld equation for Couette flow -- 5.6.4 Instability due to linear resonance -- 6 Instabilities at low Reynolds number -- 6.1 Introduction -- 6.2 Films falling down an inclined plane -- 6.2.1 Base flow and characteristic scales -- 6.2.2 Formulation of the stability problem -- 6.2.3 A long-wave interfacial instability -- 6.2.4 The instability mechanism -- 6.2.5 Experimental study -- 6.2.6 Instability of the wall mode at small slope -- 6.3 Sheared liquid films -- 6.3.1 Introduction -- 6.3.2 The long-wave instability mechanism -- 6.3.3 Waves of shorter wavelength -- 6.3.4 Instability of a falling film revisited. | |
| 505 | 8 | |a 6.4 Exercises -- 6.4.1 Critical slope for a falling film -- 6.4.2 Boundary conditions on a free interface -- 6.4.3 Solution for long waves -- 6.4.4 Stability using the depth-averaged equations -- 7 Avalanches, ripples, and dunes -- 7.1 Introduction -- 7.2 Avalanches -- 7.2.1 Particle flow on a rough inclined plane -- 7.2.2 Linear stability -- 7.2.3 Experiments -- 7.3 Sediment transport by a flow -- 7.3.1 Dimensional analysis -- 7.3.2 The speed of mobile particles -- 7.3.3 The number density of mobile particles -- 7.3.4 The particle flux -- 7.3.5 Particle relaxation effects -- 7.4 Ripples and dunes: a preliminary dimensional analysis -- 7.4.1 Aeolian ripples and dunes -- 7.4.2 Subaqueous ripples and dunes -- 7.5 Subaqueous ripples under a continuous flow -- 7.5.1 Phase advance of the shear stress -- 7.5.2 Instability -- 7.5.3 Discussion -- 7.6 Subaqueous ripples in oscillating flow -- 7.6.1 Introduction -- 7.6.2 Observations -- 7.6.3 Steady streaming over a wavy bottom -- 7.6.4 Instability -- 7.7 Subaqueous dunes -- 7.7.1 Introduction -- 7.7.2 A simple model -- 7.7.3 Stability on a flat rigid bed -- 7.7.4 Stability on an erodible bed -- 7.8 Exercises -- 7.8.1 Stability of an avalanche -- 7.8.2 Stability of a river flow over a flat bed -- 7.8.3 Dunes: constant friction coefficient -- 7.8.4 Dunes: nonconstant friction coefficient -- 8 Nonlinear dynamics of systems with few degrees of freedom -- 8.1 Introduction -- 8.2 Nonlinear oscillators -- 8.2.1 A strongly dissipative oscillator in a double-well potential -- 8.2.2 The van der Pol oscillator: amplitude saturation -- 8.2.3 The Duffing oscillator: the frequency correction -- 8.2.4 Forced oscillators -- 8.3 Systems with few degrees of freedom -- 8.3.1 A model equation -- 8.3.2 The amplitude equations -- 8.3.3 Reduction of the dynamics near threshold -- 8.4 Illustration: instability of a sheared interface. | |
| 505 | 8 | |a 8.5 Exercises -- 8.5.1 The van der Pol--Duffing oscillator -- 8.5.2 The van der Pol oscillator: restabilization -- 8.5.3 The van der Pol oscillator: frequency locking -- 8.5.4 The van der Pol oscillator subject to a constant forcing -- 8.5.5 The parametrically forced oscillator -- 8.5.6 Weakly nonlinear dynamics of the KS--KdV equation -- 9 Nonlinear dispersive waves -- 9.1 Introduction -- 9.2 Instability of gravity waves -- 9.2.1 Stokes waves -- 9.2.2 The Benjamin--Feir instability -- 9.3 Instability due to resonant interactions -- 9.3.1 The model problem -- 9.3.2 A nonlinear Klein--Gordon wave -- 9.3.3 Instability of a monochromatic nonlinear wave -- 9.4 Instability to modulations -- 9.4.1 Linear dynamics of a wave packet: envelope equation -- 9.4.2 Nonlinear dynamics: the nonlinear Schrödinger equation -- 9.4.3 Stability of a quasi-monochromatic wave -- 9.4.4 Interpretation in terms of phase instability -- 9.4.5 Derivation of the NLS equation for the Klein--Gordon wave -- 9.5 Resonances revisited -- 9.6 Exercises -- 9.6.1 A nonlinear wave including two harmonics (1) -- 9.6.2 A nonlinear wave including two harmonics (2) -- 9.6.3 A nonlinear Korteweg--de Vries wave -- 10 Nonlinear dynamics of dissipative systems -- 10.1 Introduction -- 10.2 Weakly nonlinear dynamics -- 10.2.1 Linear evolution of a wave packet -- 10.2.2 Weakly nonlinear effects: the Ginzburg--Landau equation -- 10.2.3 Example of the derivation of the Ginzburg--Landau equation -- 10.3 Saturation of the primary instability -- 10.4 The Eckhaus secondary instability -- 10.4.1 The instability criterion -- 10.4.2 Interpretation in terms of phase dynamics -- 10.4.3 Some experimental illustrations -- 10.5 Instability of a traveling wave -- 10.5.1 Evolution of a wave packet -- 10.5.2 A nonlinear wave -- 10.5.3 The Benjamin--Feir--Eckhaus instability. | |
| 505 | 8 | |a 10.5.4 Tollmien--Schlichting waves and the transition to turbulence. | |
| 520 | |a This modern account brings the subject to life by emphasising the physical mechanisms involved. Contains exercises and useful references. | ||
| 588 | |a Description based on publisher supplied metadata and other sources. | ||
| 590 | |a Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. | ||
| 650 | 0 | |a Unsteady flow (Fluid dynamics). | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a de Forcrand-Millard, Patricia. | |
| 776 | 0 | 8 | |i Print version: |a Charru, François |t Hydrodynamic Instabilities |d Cambridge : Cambridge University Press,c2011 |z 9780521769266 |
| 797 | 2 | |a ProQuest (Firm) | |
| 830 | 0 | |a Cambridge Texts in Applied Mathematics | |
| 856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/well/detail.action?docID=774989 |z Click to View |