Physics of Rotating Fluids

✍ Scribed by Christoph Egbers (editor), Gerd Pfister (editor)

• Publisher: Springer
• Year: 2000
• Tongue: English
• Leaves: 427
• Edition: 2000
• Category: Library

✦ Synopsis

This book is devoted to recent developments in the field of rotating fluids, in particular the study of Taylor--Couette flow, spherical Couette flow, planar Couette flow, as well as rotating annulus flow. Besides a comprehensive overview of the current state of the art, possible future directions in this research field are investigated. The first part of this volume presents several new results in the classical Taylor--Couette system covering diverse theoretical, experimental and numerical work on bifurcation theory, influence of boundary conditions, counter-rotating flows, spiral vortices and many others. The second part focuses on spherical Couette flows, including isothermal flows, thermal convective motion, as well as magnetohydrodynamics in spherical shells. The remaining parts are devoted to Goertler vortices, rotating annulus flows, as well as superfluid Couette flows. The present book will be of interest to all researchers and graduate students working actively in the field.

✦ Table of Contents

Chapter 1
1 Introduction
2 A numerical bifurcation method
2.1 Governing equations
2.2 The finite element technique
2.3 Spatial discretisation and symmetry
2.4 Stability
2.5 Bifurcation points and extended systems
3 Results
3.1 Experimental apparatus
3.2 Numerical and experimental bifurcation set
4 Discussion
References
Chapter 2
1 Introduction
2 Experimental setup
3 Measurement techniques
3.1 PIV
3.2 LDV
4 Numerical method
5 Results
5.1 Symmetric system
5.2 Asymmetric system
6 Conclusions
Acknowledgements
References
Chapter 3
1 Introduction
2 Experimental setup
3 Stability diagram
4 Primary instabilities
4.1 Transition to Taylor vortex .ow (TVF)
4.2 Transition to time –dependent flow states
5 Transition from Spirals to TVF
6 Wavy –vortex flow
7 Observation of propagating Taylor vortices
8 Comparison to theoretical investigations
9 Conclusion
Acknowledgements
References
Chapter 4
1 Introduction
2 System
3 Linear stability analysis of CCF
4 Bifurcation properties of Taylor vortex and spiral .ow
5 Structure of Taylor vortex and spiral .ow
6 Summary
Acknowledgements
References
Chapter 5
1 Introduction
2 Modulated base .ow
2.1 Narrow gap approximation
3 Stability problem
3.1 Perturbative analysis
4 Nonlinear models
4.1 Amplitude equations
4.2 Lorenz model
5 Conclusions
References
Chapter 6
1 Introduction
2 Experimental setup
3 An intermittency route to chaos
3.1 Onset of ‘symmetric ’chaos
3.2 Type of intermittency
3.3 Observation of Shil ’nikov attractor
3.4 Transition to Hopf regime
4 A T^3 -torus in spatial inhomogeneous flow
4.1 Axially localised Large-jet mode
4.2 Onset of VLF mod and transition to chaos
5 Discussion
References
Chapter 7
1 Introduction
2 Pomeau model of spatiotemporal intermittency
2.1 Analogy with the directed percolation
2.2 Ginzburg –Landau amplitude equation
3 STI in the Taylor –Dean system
3.1 Main results on critical properties
3.2 STI in other extended systems
4 STI in the Couette –Taylor system
4.1 Experimental setup
4.2 Results
4.3 Physical origin of turbulent bursts
4.4 Kinematics of turbulent spiral
4.5 Hayot –Pomeau model for spiral turbulence
5 Conclusion
6 Acknowledgements
References
Chapter 8
1 Introduction
2 Spiral –Couette flow
2.1 Linear stability of the SCF
2.2 Computation of the neutral stability curves


3 Spiral –Poiseuille flow

4 Conclusions
References
Chapter 9
1 Introduction
2 Cylindrical Couette flow with an imposed axial flow
2.1 Stability
2.2 Velocity field
3 Cylindrical Couette flow with an imposed radial flow
4 Combined radial and axial flow
5 Summary
References
Chapter 10
1 Introduction
1.1 Magnetic fluids
1.2 Magnetic properties of ferro fluids
1.3 Viscous properties of ferro fluids
2 Taylor vortex flow in magnetic fluids
2.1 Taylor vortex flow as a tool for magnetic fluid characterization
2.2 Changes of the flow profile in magnetic fields
3 Taylor vortex flow in magnetic fluids with radial heat gradient
4 Conclusion and outlook
References
Chapter 11
1 Stationary Taylor-vortex flows
2 Convection rolls with stress-free boundaries
2.1 Critical curves of the primary solution
2.2 Pure-mode solutions
3 Secondary bifurcations on pure mode solutions
3.1 The 2-roll,4-roll interaction in a model problem
3.2 The perturbation approach
3.3 A Hopf curve
3.4 The 2-roll,6-roll interaction in a model problem
3.5 Other interactions
4 Numerical investigations
4.1 The Rayleigh –Bénard code used
4.2 Convection rolls with rigid boundaries on top and bottom
4.3 Secondary bifurcations in the Taylor problem revisited
References
Chapter 12
1 Introduction
2 Flow between cones with a constant width of the gap
2.1 Experimental set-up
2.2 Flow field and Taylor vortices
2.3 In .uence of initial and boundary conditions
3 Combinations of circular and conical cylinders
3.1 Rotating cylinder in a cone
3.2 Rotating cone in a cylinder
4 Flow between cones with different apex angles
5 Flow between rotating ellipsoids
5.1 Oblate rotating ellipsoids
5.2 Prolate rotating ellipsoids
6 Conclusions
References
Chapter 13
1 Introduction
2 Summary of previous investigations
3 Experimental methods
3.1 Spherical Couette flow apparatus
3.2 LDV measuring system and visualisation methods
4 Transitions
4.1 Small and medium gap instabilities
4.2 Bifurcation behaviour
4.3 Wide gap instabilities
5 Conclusion
Acknowledgements
References
Chapter 14
1 Introduction
2 Onset Reynolds numbers of various disturbances
3 Structure and formation of the spiral TG vortices
4 Motion of the azimuthally travelling waves
5 Spectral analysis of velocity fluctuations
6 Relaminarization
7 Concluding remarks
References
Chapter 15
1 Introduction
2 Numerical simulations
3 Experiments
4 Conclusion
References
Chapter 16
1 Introduction
2 Mathematical formulation
3 Results and discussion
3.1 Axisymmetric basic flow
3.2 Three-dimensional convective motions
3.3 Transient evolution
4 Concluding remarks
References
Chapter 17
1 Introduction
2 The induction equation
3 Kinematic dynamo action
4 The Lorentz force
5 Magnetic Couette flow
References
Chapter 18
1 Introduction
2 Heteroclinic cycles in systems with O (3)symmetry and the spherical Bénard problem
3 Perturbation induced by a slow rotation of the domain
References
Chapter 19
Part I. Active control over secondary instability in a swept wing boundary layer
1. Introduction
2. Experimental procedure and equipment
3. Measurement results
3.1. Characteristics of waves developing on a group of vortices
3.2. Interaction between the neighbouring vortices
3.3. Propagation of travelling disturbances in a system of vortices
4. Study of mutual cancellation of the waves
5. Localized continuous suction
Part II. Transition and control experiments in a boundary layer with Görtler-like vortices
1. Introduction
2. Transition experiments in a boundary layer with Görtler-like vortices
3. The effect of roughness–induced vortices
3.1. Instability and breakdown to turbulence
4. Controlled excitation of the instability
4.1. Development of small amplitude travelling waves
Discussion
PART III. Influence of riblets on a boundary layer with Görtler-like vortices
References
Chapter 20
1 Introduction
2 The rotating annulus experiment
3 Stability
4 Nonlinear dynamics
4.1 Measurement technique
4.2 Flow characterization
4.3 Bifurcation scenario
4.4 Comparison to Taylor –Couette flow
5 Conclusions
Acknowledgements
References
Chapter 21
1 Liquid helium
2 Helium II and Landau ’s two-fluid model
3 Vortex lines and the breakdown of Landau ’s model
4 The generalized Landau equations
5 The basic state
6 Rotations of the inner cylinder:absolute zero
7 Rotations of the inner cylinder: finite temperatures
8 Rotations of the inner cylinder: nonlinear effects
9 Rotations of the outer cylinder
10 Co-rotations and counter-rotations of the cylinders
11 Finite aspect ratios and end effects
12 Discussion and outlook
References
Chapter 22
1 Introduction
2 Mathematical formulation of the problem
3 Steady three-dimensional wavy roll solutions in an air layer
4 Wavy roll solutions in dependence on the Grashof number
5 Transition to quaternary states of fluid flow
6 Concluding remarks
References
Chapter 23
1 Introduction
2 Isotherm, steady flow of a Newtonian fluid
2.1 Governing equations
2.2 Von Kármán ’s solution for a single rotating disk
2.3 Flow between co-rotating disks
3 Conclusions and future investigations
References