ISBN: 3540675140
TITLE: Physics of Rotating Fluids
AUTHOR: Egbers, Christoph; Pfister, Gerd (Eds.)
TOC:

Part I TaylorCouette flow
Pitchfork bifurcations in small aspect ratio TaylorCouette flow
Tom Mullin, Doug Satchwell, Yorinobu Toya 3
1 Introduction 3
2 A numerical bifurcation method 7
2.1 Governing equations 7
2.2 The finite element technique 9
2.3 Spatial discretisation and symmetry 11
2.4 Stability 13
2.5 Bifurcation points and extended systems 15
3 Results 16
3.1 Experimental apparatus 16
3.2 Numerical and experimental bifurcation set 17
4 Discussion 18
References 19
TaylorCouette system with asymmetric boundary conditions
Oliver Meincke, Christoph Egbers, Nicoleta Scurtu, Eberhard Bnsch 22
1 Introduction 22
2 Experimental setup 23
3 Measurement techniques 23
3.1 PIV 23
3.2 LDV 25
4 Numerical method 26
5 Results 27
5.1 Symmetric system 27
5.2 Asymmetric system 30
6 Conclusions 34
References 35
Bifurcation and structure of flow between counter-rotating cylinders
Arne Schulz, Gerd Pfister 37
1 Introduction 37
2 Experimental setup 37
3 Stability diagram 39
4 Primary instabilities 40
4.1 Transition to Taylor vortex flow (TVF) 40
4.2 Transition to time-dependent flow states 42
5 Transition from Spirals to TVF 45
6 Wavy-vortex flow 46
7 Observation of propagating Taylor vortices 50
8 Comparison to theoretical investigations 51
9 Conclusion 53
References 53
Spiral vortices and Taylor vortices in the annulus between counter-rotating cylinders
Christian Hoffmann, Manfred Lcke 55
1 Introduction 55
2 System 56
3 Linear stability analysis of CCF 57
4 Bifurcation properties of Taylor vortex and spiral flow 58
5 Structure of Taylor vortex and spiral flow 64
6 Summary 64
References 66
Stability of time-periodic flows in a TaylorCouette geometry
Christiane Normand 67
1 Introduction 67
2 Modulated base flow 71
2.1 Narrow gap approximation 73
3 Stability problem 74
3.1 Perturbative analysis 76
4 Nonlinear models 77
4.1 Amplitude equations 77
4.2 Lorenz model 79
5 Conclusions 81
References 82
Low-dimensional dynamics of axisymmetric modes in wavy Taylor vortex flow
Jan Abshagen, Gerd Pfister 84
1 Introduction 84
2 Experimental setup 86
3 An intermittency route to chaos 86
3.1 Onset of 'symmetric' chaos 87
3.2 Type of intermittency 90
3.3 Observation of Shil'nikov attractor 92
3.4 Transition to Hopf regime 94
4 A T^3-torus in spatial inhomogeneous flow 96
4.1 Axially localised Large-jet mode 96
4.2 Onset of VLF mode and transition to chaos 98
5 Discussion 100
References 100
Spatiotemporal intermittency in TaylorDean and CouetteTaylor systems
Innocent Mutabazi, Afshin Goharzadeh and Patrice Laure 102
1 Introduction 102
2 Pomeau model of spatiotemporal intermittency 103
2.1 Analogy with the directed percolation 104
2.2 GinzburgLandau amplitude equation 106
3 STI in the TaylorDean system 107
3.1 Main results on critical properties 107
3.2 STI in other extended systems 108
4 STI in the CouetteTaylor system 109
4.1 Experimental setup 109
4.2 Results 111
4.3 Physical origin of turbulent bursts 112
4.4 Kinematics of turbulent spiral 113
4.5 HayotPomeau model for spiral turbulence 115
5 Conclusion 116
6 Acknowledgments 116
References 116
Axial effects in the TaylorCouette problem: SpiralCouette and SpiralPoiseuille flows
lvaro Meseguer, Francesc Marqus 118
1 Introduction 118
2 SpiralCouette flow 119
2.1 Linear stability of the SCF 121
2.2 Computation of the neutral stability curves 122
2.3 Stability analysis for eta = 0.5 122
2.4 Comparison with experimental results (eta = 0.8) 127
3 SpiralPoiseuille flow 130
3.1 Linear stability results (eta = 0.5) 131
4 Conclusions 133
References 135
Stability and experimental velocity field in TaylorCouette flow with an axial and radial flow
Richard M. Lueptow 137
1 Introduction 137
2 Cylindrical Couette flow with an imposed axial flow 139
2.1 Stability 139
2.2 Velocity field 143
3 Cylindrical Couette flow with an imposed radial flow 148
4 Combined radial and axial flow 150
5 Summary 153
References 154
Transport phenomena in magnetic fluids in cylindrical geometry
Stefan Odenbach 156
1 Introduction 156
1.1 Magnetic fluids 157
1.2 Magnetic properties of ferrofluids 158
1.3 Viscous properties of ferrofluids 160
2 Taylor vortex flow in magnetic fluids 163
2.1 Taylor vortex flow as a tool for magnetic fluid characterization 163
2.2 Changes of the flow profile in magnetic fields. 167
3 Taylor vortex flow in magnetic fluids with radial heat gradient 169
4 Conclusion and outlook 169
References 170
Secondary bifurcations of stationary flows
Rita Meyer-Spasche, John H. Bolstad, Frank Pohl 171
1 Stationary Taylor-vortex flows 171
2 Convection rolls with stress-free boundaries 172
2.1 Critical curves of the primary solution 174
2.2 Pure-mode solutions 175
3 Secondary bifurcations on pure mode solutions 177
3.1 The 2-roll,4-roll interaction in a model problem 177
3.2 The perturbation approach 179
3.3 A Hopf curve 180
3.4 The 2-roll, 6-roll interaction in a model problem 181
3.5 Other interactions 183
4 Numerical investigations 184
4.1 The RayleighBnard code used 184
4.2 Convection rolls with rigid boundaries on top and bottom 187
4.3 Secondary bifurcations in the Taylor problem revisited 191
References 193
Taylor vortices at different geometries
Manfred Wimmer 194
1 Introduction 194
2 Flow between cones with a constant width of the gap 195
2.1 Experimental set-up 195
2.2 Flow field and Taylor vortices 195
2.3 Influence of initial and boundary conditions 198
3 Combinations of circular and conical cylinders 200
3.1 Rotating cylinder in a cone 201
3.2 Rotating cone in a cylinder 201
4 Flow between cones with different apex angles 203
5 Flow between rotating ellipsoids 206
5.1 Oblate rotating ellipsoids 209
5.2 Prolate rotating ellipsoids 210
6 Conclusions 211
References 212
Part II Spherical Couette flow
Isothermal spherical Couette flow
Markus Junk, Christoph Egbers 215
1 Introduction 215
2 Summary of previous investigations 218
3 Experimental methods 220
3.1 Spherical Couette flow apparatus 220
3.2 LDV measuring system and visualisation methods 222
4 Transitions 224
4.1 Small and medium gap instabilities 224
4.2 Bifurcation behaviour 227
4.3 Wide gap instabilities 228
5 Conclusion 231
Vortical structures and velocity fluctuations of spiral and wavy vortices in the spherical Couette Flow
Koichi Nakabayashi, Weiming Sha 234
1 Introduction 234
2 Onset Reynolds numbers of various disturbances 235
3 Structure and formation of the spiral TG vortices 236
4 Motion of the azimuthally travelling waves 241
5 Spectral analysis of velocity fluctuations 244
6 Relaminarization 247
7 Concluding remarks 254
References 254
Spherical Couette flow with superimposed throughflow
Karl Bhler 256
1 Introduction 256
2 Numerical simulations 260
3 Experiments 260
4 Conclusion 267
References 267
Three-dimensional natural convection in a narrow spherical shell
Ming Liu, Christoph Egbers 269
1 Introduction 269
2 Mathematical formulation 270
3 Results and discussion 273
3.1 Axisymmetric basic flow 273
3.2 Three-dimensional convective motions 274
3.3 Transient evolution 287
4 Concluding remarks 291
References 292
Magnetohydrodynamic flows in spherical shells
Rainer Hollerbach 295
1 Introduction 295
2 The induction equation 296
3 Kinematic dynamo action 301
4 The Lorentz force 304
5 Magnetic Couette flow 306
References 314
Intermittency at onset of convection in a slowly rotating, self-gravitating spherical shell
Pascal Chossat 317
1 Introduction 317
2 Heteroclinic cycles in systems with O(3) symmetry and the spherical Bnard problem 318
3 Perturbation induced by a slow rotation of the domain 322
References 324
Part III Goertler vortices and curved surfaces
Control of secondary instability of the crossflow and Grtler-like vortices (Success and problems)
Viktor V. Kozlov, Genrich R. Grek 327
Part I. Active control over secondary instability in a swept wing boundary layer 327
Part II. Transition and control experiments in a boundary layer with Grtler-like vortices 336
PART III. Influence of riblets on a boundary layer with Grtler-like vortices 346
References 349
Part IV Rotating annulus
Higher order dynamics of baroclinic waves
Bernd Sitte, Christoph Egbers 355
1 Introduction 355
2 The rotating annulus experiment 357
3 Stability 359
4 Nonlinear dynamics 362
4.1 Measurement technique 362
4.2 Flow characterization 364
4.3 Bifurcation scenario 371
4.4 Comparison to TaylorCouette flow 374
5 Conclusions 374
References 375
Part V Plane Couette flow
Superfluid Couette flow
Carlo F. Barenghi 379
1 Liquid helium 379
2 Helium II and Landau's two-fluid model 379
3 Vortex lines and the breakdown of Landau's model 381
4 The generalized Landau equations 383
5 The basic state 386
6 Rotations of the inner cylinder: absolute zero 389
7 Rotations of the inner cylinder: finite temperatures 390
8 Rotations of the inner cylinder: nonlinear effects 394
9 Rotations of the outer cylinder 394
10 Co-rotations and counter-rotations of the cylinders 396
11 Finite aspect ratios and end effects 396
12 Discussion and outlook 397
References 398
Tertiary and quaternary solutions for plane Couette flow with thermal stratification
R.M. Clever, Friedrich H. Busse 399
1 Introduction 399
2 Mathematical formulation of the problem 401
3 Steady three-dimensional wavy roll solutions in an air layer 404
4 Wavy roll solutions in dependence on the Grashof number 408
5 Transition to quaternary states of fluid flow 413
6 Concluding remarks 414
References 416
On the rotationally symmetric laminar flow of Newtonian fluids induced by rotating disks
Antonio Delgado 417
1 Introduction 417
2 Isotherm, steady flow of a Newtonian fluid 419
2.1 Governing equations 419
2.2 Von Krmn's solution for a single rotating disk 420
2.3 Flow between co-rotating disks 422
3 Conclusions and future investigations 437
References 438
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