Thermal convection: patterns, evolution, and stability
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2010
|
| Edition: | This ed. 1 publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 670 S. Ill., graph. Darst. |
| ISBN: | 9780470699942 |
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MARC
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| 001 | BV025594672 | ||
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| 020 | |a 9780470699942 |9 978-0-470-69994-2 | ||
| 035 | |a (OCoLC)699845251 | ||
| 035 | |a (DE-599)BVBBV025594672 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
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| 084 | |a UG 2700 |0 (DE-625)145620: |2 rvk | ||
| 100 | 1 | |a Lappa, Marcello |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Thermal convection |b patterns, evolution, and stability |c Marcello Lappa |
| 250 | |a This ed. 1 publ. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2010 | |
| 300 | |a XX, 670 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 0 | 7 | |a Konvektion |0 (DE-588)4117572-4 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020190767 | ||
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| _version_ | 1804142776885968897 |
|---|---|
| adam_text | Contents
Preface
xv
Acknowledgements
xix
1
Equations, General Concepts and Methods of Analysis
1
1.1
Pattern Formation and Nonlinear Dynamics
1
1.1.1
Some Fundamental Concepts: Pattern, Interrelation and Scale
2
1.1.2
PDEs, Symmetry and Nonequilibrium Phenomena
4
1.2
The Navier-Stokes Equations
6
1.2.1
A Satisfying Microscopic Derivation of the Balance Equations
6
1.2.2
A Statistical Mechanical Theory of Transport Processes
7
1.2.3
The Continuity Equation
9
1.2.4
The Momentum Equation
10
1.2.5
The Total Energy Equation
11
1.2.6
The Budget of Internal Energy
13
1.2.7
Newtonian Fluids
13
1.2.8
Some Considerations About the Dynamics of Vorticity
15
1.2.9
Incompressible Formulation of the Balance Equations
18
1.2.10
Nondimensional Form of the Equations for Thermal Problems
19
1.3
Energy Equality and
Dissipati ve
Structures
21
1
.4
Flow Stability, Bifurcations and Transition to Chaos
25
1.5
Linear Stability Analysis: Principles and Methods
27
1.5.1
Conditional Stability and Infinitesimal Disturbances
27
1.5.2
The Exponential Matrix and the Eigenvalue Problem
28
1.5.3
Linearization of the
Navier—
Stokes Equations
30
1.5.4
A Simple Example: The Stability of a Parallel Flow with an
Inflectional Velocity Profile
32
1.5.5
Weaknesses and Limits of the Linear Stability Approach
35
1.6
Energy Stability Theory
36
1.6.1
A Global Budget for the Generalized Disturbance Energy
36
1.6.2
The
Extrémům
Problem
39
1.7
Numerical Integration of the Navier-Stokes Equations
40
1.7.1
Vorticity Methods
4]
1.7.2
Primitive Variables Methods
42
1.8
Some Universal Properties of Chaotic States
46
1.8.1 Feigenbaum,
Ruelle-Takens and Manneville-Pomeau Scenarios
46
viii Contents
1.8.2
Phase Trajectories,
Attractors and Strange Attractors 47
1.8.3 The Lorenz Model
and the Butterfly Effect
48
1.8.4
A Possible Quantification of SIC: The Lyapunov Spectrum
51
1.8.5
The Mandelbrot Set: The Ubiquitous Connection Between Chaos and
Fractals
53
1.9
The Maxwell Equations
58
2
Classical Models, Characteristic Numbers and Scaling Arguments
63
2.1
Buoyancy Convection and the Boussinesq Model
64
2.2
Convection in Space
66
2.2.1
A Definition of Microgravity
66
2.2.2
Experiments in Space
67
2.2.3
Surface Tension-driven Flows
68
2.2.4
Acceleration Disturbances on Orbiting Platforms and Vibrational
Flows
68
2.3
Marangoni
Flow
70
2.3.1
The Genesis and Relevant Nondimensional Numbers
71
2.3.2
Microzone
Facilities and
Microscale
Experimentation
75
2.3.3
A Paradigm Model: The Liquid Bridge
75
2.4
Exact Solutions of the Navier-Stokes Equations for Thermal Problems
78
2.4.1
Thermogravitational Convection: The Hadley Flow
80
2.4.2
Marangoni
Flow
80
2.4.3
Hybrid States
83
2.4.4
General Properties
83
2.4.5
The Infinitely Long Liquid Bridge
85
2.4.6
Inclined Systems
86
2.5
Conductive, Transition and Boundary-layer Regimes
89
3
Examples of Thermal Fluid Convection and Pattern Formation in Nature and
Technology
95
3.1
Technological Processes: Small-scale Laboratory and Industrial Setups
95
3.1.1
Crystal Growth from the Melt: Typical Techniques
96
3.1.2
Detrimental Effects Induced by
Convective
Phenomena
101
3.2
Examples of Thermal Fluid Convection and Pattern Formation at the
Mesoscale
103
3.3
Planetary Structure and Dynamics: Convective Phenomena
103
3.3.1
Earth s Layered Structure
103
3.3.2
Earth s Mantle Convection
104
3.3.3
Plate Tectonics Theory
104
3.3.4
Earth s Core Convection
106
3.3.5
The Icy Galilean Satellites
107
3.4
Atmospheric and Oceanic Phenomena
108
3.4.1
A Fundamental Model: The Hadley Circulation
108
3.4.2
Mesoscale Shallow Cellular Convection: Collection of Clouds and
Related Patterns
110
Contents ix
3.4.3
The Planetary Boundary Layer
112
3.4.4
Atmospheric Convection in Other Solar System Bodies
116
4
Thermogravitational Convection: The
Rayleigh-Bénard
Problem
119
4.1
Nonconfined Fluid Layers and Ideal Straight Rolls
119
4.1.1
The Linearized Problem: Primary Convective Modes
119
4.1.2
Systems Heated from Above: Internal Gravity Waves
122
4.2
The
Busse
Balloon
124
4.2.1
Toroidal-Poloidal Decomposition
125
4.2.2
The Zoo of Secondary Modes
127
4.3
Some Considerations About the Role of Dislocation Dynamics
133
4.4
Tertiary and Quaternary Modes of Convection
135
4.5
Spoke Pattern Convection
138
4.6
Spiral Defect Chaos, Hexagons and Squares
142
4.7
Convection with Lateral Walls
149
4.8
Two-dimensional Models
151
4.8.1
Distinct Modes of Convection and Possible Symmetries
151
4.8.2
Higher Modes of Convection and Oscillatory Regimes
155
4.9
Three-dimensional Parallelepipedic Enclosures: Classification of Solutions and
Possible Symmetries
157
4.9.1
The Cubical Box
160
4.9.2
The Onset of Time Dependence
161
4.10
The Circular Cylindrical Problem
165
4.10.1
Moderate Aspect Ratios: Azimuthal Structure and Effect of Lateral
Boundary Conditions
165
4.10.2
Small Aspect Ratios: Targets and Pan Am Textures
170
4.11
Spirals: Genesis, Properties and Dynamics
173
4.11.1
The Archimedean Spiral
175
4.11.2
Spiral Wavenumber
175
4.11.3
Multi-armed Spirals and Spiral Core Instability
176
4.12
From Spirals to SDC: The Extensive Chaos Problem
179
4.13
Three-dimensional Convection in a Spherical Shell
182
4.13.1
Possible Patterns of Convection and Related Symmetries
183
4.13.2
The Heteroclinic Cycles
183
4.13.3
The Highly Viscous Case
185
4.13.4
The Geodynamo Problem
188
5
The Dynamics of Thermal Plumes and Related Regimes of Motion
195
5.1
Introduction
195
5.2
Free Plume Regimes
196
5.2.1
The Diffusive-Viscous Regime
197
5.2.2
The Viscous-Nondiffusive Regime
198
5.2.3
The Inviscid-Diffusive Regime
198
5.2.4
The Inviscid-Nondiffusive Regime
200
5.2.5
Sinuous Instabilities Created by Horizontal Shear
200
Contents
5.2.6 Geometrie
Constraints
201
5.3
The Flywheel Mechanism: The Wind of Turbulence
202
5.3.1
Upwelling and Downward Jets and Alternating Eruption of Thermal
Plumes
203
5.3.2
Geometric Effects
204
5.3.3
The Origin of the Large-scale Circulation: The Childress and
Villermaux Theories
205
5.3.4
The Role of Thermal Diffusion in Turbulent
Rayleigh-Bénard
Convection
208
5.4
Multiplume Configurations Originated from Discrete Sources of Buoyancy
208
6
Systems Heated from the Side: The Hadley Flow
215
6.1
The Infinite Horizontal Layer
215
6.1.1
The Hadley Flow and its General Perturbing Mechanisms
216
6.1.2
Hydrodynamic Modes and Oscillatory Longitudinal Rolls
219
6.1.3
The Rayleigh Mode
223
6.1.4
Competition of Disturbances and Tertiary Modes of Convection
225
6.2
Two-dimensional Horizontal Enclosures
228
6.2.1
Geometric Constraints and Multiplicity of Solutions
228
6.2.2
Instabilities Originating from Boundary Layers and Patterns with
Internal Waves
235
6.3
The Infinite Vertical Layer: Cats-eye Patterns and Temperature Waves
247
6.4
Three-dimensional Parallelepipedic Enclosures
253
6.5
Cylindrical Geometries under Various Heating Conditions
262
7
Thermogravitational Convection in Inclined Systems
271
7.1
Inclined Layer Convection
272
7.1.1
The Codimension-two Point
273
7.1.2
Tertiary and High-order Modes of Convection
275
7.2
Inclined Side-heated Slots
279
7.2.1
Stationary Longitudinal Long-wavelength Instability
281
7.2.2
Stationary Transversal Instability
282
7.2.3
Oscillatory Transversal Long-wavelength Instability
284
7.2.4
Stationary Longitudinal Short-wavelength Instability
284
7.2.5
Oscillatory Longitudinal Instability
284
7.2.6
Interacting Longitudinal and Transversal Multicellular Modes
286
8
Thermovibrational Convection
289
8.1
Equations and Relevant Parameters
289
8.2
Fields Decomposition
290
8.3
The TFD Distortions
291
8.4
High Frequencies and the Thermovibrational Theory
293
8.5
States of Quasi-equilibrium and Related Stability
294
8.5.1
The Vibrational Hydrostatic Conditions
294
Contents xi
8.5.2 The Linear
Stability
Problem 295
8.5.3 Solutions
for the
Infinite
Layer
297
8.6
Primary and Secondary Patterns of Symmetry
299
8.7
Medium and Low Frequencies: Possible Regimes and Flow Patterns
303
8.7.1
Synchronous, Subharmonic and Nonperiodic Response
303
8.7.2
Reduced Equations and Related Ranges of Validity
305
9
Marangoni-Bénard
Convection
317
9.1
Introduction
317
9.2
High Prandtl Number Liquids: Patterns with Hexagons, Squares and Triangles
320
9.3
Liquid Metals: Inverted Hexagons and High-order Solutions
325
9.4
Effects of Lateral Confinement
326
9.4.1
Circular Containers
328
9.4.2
Rectangular Containers
331
9.5
Temperature Gradient Inclination
334
10
Thermocapillary Convection
341
10.1
Basic Features of Steady
Marangoni
Convection
342
10.2
Stationary Multicellular Flow and
Hydrothermal
Waves
345
10.2.1
Basic Velocity Profiles: The Linear and Return Flows
346
10.2.2
Linear Stability Analysis
346
10.2.3
Weakly Nonlinear Analysis
354
10.2.4
Boundary Effects: 2D and
3D
Numerical Studies
359
10.3
Annular Configurations
368
10.4
The Liquid Bridge
375
10.4.1
Historical Perspective
375
10.4.2
Liquid Metals and Semiconductor Melts
378
10.4.3
The First Bifurcation: Structure of the Secondary
3D
Steady Flow
379
10.4.4
Effect of Geometric Parameters
381
10.4.5
A Generalized Theory for the Azimuthal Wavenumber
389
10.4.6
The Second Bifurcation: Tertiary Modes of Convection
390
10.4.7
High Prandtl Number Liquids
393
10.4.8
Standing Waves and Travelling Waves
399
10.4.9
Symmetric and Asymmetric Oscillatory Modes of Convection
407
10.4.10
System Dynamic Evolution
412
10.4.11
The
Hydrothermal
Mechanism in Liquid Bridges
417
10.4.12
Noncylindrical Liquid Bridges
421
10.4.13
The Intermediate Range of Prandtl Numbers
423
11
Mixed Buoyancy-Marangoni Convection
427
11.1
The Canonical Problem: The Infinite Horizontal Layer
429
11.2
Finite-sized Systems Filled with Liquid Metals
436
11.3
Typical Terrestrial Laboratory Experiments with Transparent Liquids
449
11.4
The Rectangular Liquid Layer
450
xii Contents
11.4.1
Waves and Multicellular Patterns
450
11.4.2
Tertiary Modes of Convection: OMC and HTW with
Spatiotemporal
Dislocations
456
11.5
Effects Originating from the Walls
458
11.5.1
Lateral Boundaries as a Permanent Stationary Disturbance
459
11.5.2
Collision Phenomena of HTW and Wall-generated Steady Patterns
460
11.5.3
Streaks Generated by a Lift-up Process and Instabilities of a
Mechanical Nature
464
11.6
The Open Vertical Cavity
468
11.6.1
Volume Driving Actions and Rising Thermal Plumes
470
11.6.2
Aiding
Marangoni
and Buoyant Flows
470
11.6.3
Counteracting Driving Forces and Separation Phenomena
472
11.6.4
Surface Driving Actions and Vertical Temperature Gradients
474
11.7
The Annular Pool
475
11.7.1
Target-like Wave Patterns (HW2)
476
11.7.2
Waves with Spiral Pattern (HW,)
478
11.7.3
Stationary Radial Rolls
480
11.7.4
Progression Towards Chaos and Fractal Behaviour
483
11.7.5
The Reverse Annular Configuration: Incoherent Spatial Dynamics
487
11.7.6
Some Considerations About the Role of Curvature, Heating Direction
and Gravity
488
11.8
The Liquid Bridge on the Ground
491
11.8.1
Microscale
Experiments
492
11.8.2
Heating from Above or from Below
499
11.8.3
The Route to Aperiodicity
510
12
Hybrid Regimes with Vibrations
517
12.1
RB Convection with Vertical Shaking
519
12.2
Complex Order, Quasi-periodic Crystals and Superlattices
525
12.2.1
Purely Harmonic Patterns
527
12.2.2
Purely Subharmonic Patterns
529
12.2.3
Coexistence and Complex Order
529
12.3
RB Convection with Horizontal or Oblique Shaking
533
12.4
Laterally Heated Systems and Parametric Resonances
538
12.4.1
The Infinite Horizontal Layer
538
12.4.2
Domains with Vertical Walls
544
12.4.3
The Infinite Vertical Layer
548
12.4.4
Inclined Systems
550
12.5
Control of Thermogravitational Convection
550
12.5.1
Cell Orientation as a Means to Mitigate Convective Disturbances on
Orbiting Platforms
551
12.5.2
Control of Convection Patterning and Intensity in Shallow Enclosures
553
12.5.3
Modulation of Thermal Boundary Conditions
559
12.6
Mixed Marangoni-Thermovibrational Convection
561
12.6.1
Basic Solutions
561
Contents xiii
12.6.2
Control
of Convection Patterning and Intensity in Shallow Enclosures
566
12.6.3
Control of
Hydrothermal
Waves
567
12.7
Modulation of
Marangoni-Bénard
Convection
575
13
Flow Control by Magnetic Fields
581
13.1
Static and Uniform Magnetic Fields
582
13.1.1
Physical Principles and Governing Equations
582
13.1.2 Hartmann
Boundary Layers
584
13.2
Historical Developments and Current Status
584
13.2.1
Stabilization of Thermogravitational Flows
584
13.2.2
Stabilization of Surface Tension-driven Flows
597
13.3
Rotating Magnetic Fields
604
13.4
Gradients of Magnetic Fields and Virtual Microgravity
607
References
609
Index
659
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| id | DE-604.BV025594672 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:37:09Z |
| institution | BVB |
| isbn | 9780470699942 |
| language | English |
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| spelling | Lappa, Marcello Verfasser aut Thermal convection patterns, evolution, and stability Marcello Lappa This ed. 1 publ. Chichester Wiley 2010 XX, 670 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Konvektion (DE-588)4117572-4 gnd rswk-swf Konvektion (DE-588)4117572-4 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020190767&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lappa, Marcello Thermal convection patterns, evolution, and stability Konvektion (DE-588)4117572-4 gnd |
| subject_GND | (DE-588)4117572-4 |
| title | Thermal convection patterns, evolution, and stability |
| title_auth | Thermal convection patterns, evolution, and stability |
| title_exact_search | Thermal convection patterns, evolution, and stability |
| title_full | Thermal convection patterns, evolution, and stability Marcello Lappa |
| title_fullStr | Thermal convection patterns, evolution, and stability Marcello Lappa |
| title_full_unstemmed | Thermal convection patterns, evolution, and stability Marcello Lappa |
| title_short | Thermal convection |
| title_sort | thermal convection patterns evolution and stability |
| title_sub | patterns, evolution, and stability |
| topic | Konvektion (DE-588)4117572-4 gnd |
| topic_facet | Konvektion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020190767&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lappamarcello thermalconvectionpatternsevolutionandstability |