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E-raamat: Hydrodynamic Instabilities

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Translated by , (Université Paul Sabatier (Toulouse III))
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Hydrodynamic InstabilitiesSuurem pilt
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The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. 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 dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. 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.

Written for any student, researcher or practitioner working in the area, this modern introduction brings this mathematical subject to life by emphasising the physical mechanisms involved. The book includes numerous experimental studies as well as over 150 exercises and references to video material.

Arvustused

'The author has written a remarkable textbook.' Isom H. Herron, Mathematical Reviews

Muu info

This modern account brings the subject to life by emphasising the physical mechanisms involved. Contains exercises and useful references.
Foreword x
Preface xiii
Video resources xvi
1 Introduction
1(42)
1.1 Phase space, phase portrait
1(1)
1.2 Stability of a fixed point
2(4)
1.3 Bifurcations
6(6)
1.4 Examples from hydrodynamics
12(18)
1.5 Non-normality of the linearized operator
30(6)
1.6 Exercises
36(7)
2 Instabilities of fluids at rest
43(45)
2.1 Introduction
43(1)
2.2 The Jeans gravitational instability
44(9)
2.3 The Rayleigh-Taylor interface instability
53(11)
2.4 The Rayleigh-Plateau capillary instability
64(4)
2.5 The Rayleigh-Benard thermal instability
68(8)
2.6 The Benard-Marangoni thermocapillary instability
76(3)
2.7 Discussion
79(1)
2.8 Exercises
80(8)
3 Stability of open flows: basic ideas
88(16)
3.1 Introduction
88(8)
3.2 A criterion for linear stability
96(2)
3.3 Convective and absolute instabilities
98(4)
3.4 Exercises
102(2)
4 Inviscid instability of parallel flows
104(35)
4.1 Introduction
104(3)
4.2 General results
107(9)
4.3 Instability of a mixing layer
116(10)
4.4 The Couette-Taylor centrifugal instability
126(8)
4.5 Exercises
134(5)
5 Viscous instability of parallel flows
139(32)
5.1 Introduction
139(6)
5.2 General results
145(9)
5.3 Plane Poiseuille flow
154(8)
5.4 Poiseuille flow in a pipe
162(1)
5.5 Boundary layer on a flat surface
162(7)
5.6 Exercises
169(2)
6 Instabilities at low Reynolds number
171(30)
6.1 Introduction
171(3)
6.2 Films falling down an inclined plane
174(19)
6.3 Sheared liquid films
193(6)
6.4 Exercises
199(2)
7 Avalanches, ripples, and dunes
201(45)
7.1 Introduction
201(1)
7.2 Avalanches
202(6)
7.3 Sediment transport by a flow
208(10)
7.4 Ripples and dunes: a preliminary dimensional analysis
218(2)
7.5 Subaqueous ripples under a continuous flow
220(10)
7.6 Subaqueous ripples in oscillating flow
230(8)
7.7 Subaqueous dunes
238(6)
7.8 Exercises
244(2)
8 Nonlinear dynamics of systems with few degrees of freedom
246(28)
8.1 Introduction
246(3)
8.2 Nonlinear oscillators
249(11)
8.3 Systems with few degrees of freedom
260(4)
8.4 Illustration: instability of a sheared interface
264(4)
8.5 Exercises
268(6)
9 Nonlinear dispersive waves
274(25)
9.1 Introduction
274(1)
9.2 Instability of gravity waves
275(4)
9.3 Instability due to resonant interactions
279(8)
9.4 Instability to modulations
287(7)
9.5 Resonances revisited
294(1)
9.6 Exercises
295(4)
10 Nonlinear dynamics of dissipative systems
299(27)
10.1 Introduction
299(1)
10.2 Weakly nonlinear dynamics
300(5)
10.3 Saturation of the primary instability
305(1)
10.4 The Eckhaus secondary instability
305(6)
10.5 Instability of a traveling wave
311(6)
10.6 Coupling to a field at large scales
317(6)
10.7 Exercises
323(3)
11 Dynamical systems and bifurcations
326(43)
11.1 Introduction
326(1)
11.2 Phase space and attractors
327(7)
11.3 Linear stability
334(4)
11.4 Invariant manifolds and normal forms
338(7)
11.5 Structural stability and genericity
345(6)
11.6 Bifurcations
351(14)
11.7 Exercises
365(4)
Appendix A The Saint-Venant equations
369(6)
A.1 Outflow from a slice of fluid
369(1)
A.2 Mass conservation
370(1)
A.3 Momentum conservation
371(1)
A.4 Modeling the wall friction
372(1)
A.5 Consistent depth-averaged equations
373(2)
References 375(12)
Index 387
François Charru is a Professor of Mechanics at the University of Toulouse, France, and researcher at the Institut de Mécanique des Fluides de Toulouse.
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