Thermal Convection : Patterns, Evolution and Stability

Acknowledgements.

1 Equations, General Concepts and Methods of Analysis.

1.1 Pattern Formation and Nonlinear Dynamics.

1.2 The Navier–Stokes Equations.

1.3 Energy Equality and Dissipative Structures.

1.4 Flow Stability, Bifurcations and Transition to Chaos.

1.5 Linear Stability Analysis: Principles and Methods.

1.6 Energy Stability Theory.

1.7 Numerical Integration of the Navier–Stokes Equations.

1.8 Some Universal Properties of Chaotic States.

1.9 The Maxwell Equations.

2 Classical Models, Characteristic Numbers and Scaling Arguments.

2.1 Buoyancy Convection and the Boussinesq Model.

2.2 Convection in Space.

2.3 Marangoni Flow.

2.4 Exact Solutions of the Navier–Stokes Equations for Thermal Problems.

2.5 Conductive, Transition and Boundary-layer Regimes.

3 Examples of Thermal Fluid Convection and Pattern Formation in Nature and Technology.

3.1 Technological Processes: Small-scale Laboratory and Industrial Setups.

3.2 Examples of Thermal Fluid Convection and Pattern Formation at the Mesoscale.

3.3 Planetary Structure and Dynamics: Convective Phenomena.

3.4 Atmospheric and Oceanic Phenomena.

4 Thermogravitational Convection: The Rayleigh–Bénard Problem.

4.1 Nonconfined Fluid Layers and Ideal Straight Rolls.

4.2 The Busse Balloon.

4.3 Some Considerations About the Role of Dislocation Dynamics.

4.4 Tertiary and Quaternary Modes of Convection.

4.5 Spoke Pattern Convection.

4.6 Spiral Defect Chaos, Hexagons and Squares.

4.7 Convection with Lateral Walls.

4.8 Two-dimensional Models.

4.9 Three-dimensional Parallelepipedic Enclosures: Classification of Solutions and Possible Symmetries.

4.10 The Circular Cylindrical Problem.

4.11 Spirals: Genesis, Properties and Dynamics.

4.12 From Spirals to SDC: The Extensive Chaos Problem.

4.13 Three-dimensional Convection in a Spherical Shell.

5 The Dynamics of Thermal Plumes and Related Regimes of Motion.

5.1 Introduction.

5.2 Free Plume Regimes.

5.3 The Flywheel Mechanism: The ‘Wind’ of Turbulence.

5.4 Multiplume Configurations Originated from Discrete Sources of Buoyancy.

6 Systems Heated from the Side: The Hadley Flow.

6.1 The Infinite Horizontal Layer.

6.2 Two-dimensional Horizontal Enclosures.

6.3 The Infinite Vertical Layer: Cats-eye Patterns and Temperature Waves.

6.4 Three-dimensional Parallelepipedic Enclosures.

6.5 Cylindrical Geometries under Various Heating Conditions.

7 Thermogravitational Convection in Inclined Systems.

7.1 Inclined Layer Convection.

7.2 Inclined Side-heated Slots.

8 Thermovibrational Convection.

8.1 Equations and Relevant Parameters.

8.2 Fields Decomposition.

8.3 The TFD Distortions.

8.4 High Frequencies and the Thermovibrational Theory.

8.5 States of Quasi-equilibrium and Related Stability.

8.6 Primary and Secondary Patterns of Symmetry.

8.7 Medium and Low Frequencies: Possible Regimes and Flow Patterns.

9 Marangoni–Bénard Convection.

9.1 Introduction.

9.2 High Prandtl Number Liquids: Patterns with Hexagons, Squares and Triangles.

9.3 Liquid Metals: Inverted Hexagons and High-order Solutions.

9.4 Effects of Lateral Confinement.

9.5 Temperature Gradient Inclination.

10 Thermocapillary Convection.

10.1 Basic Features of Steady Marangoni Convection.

10.2 Stationary Multicellular Flow and Hydrothermal Waves.

10.3 Annular Configurations.

10.4 The Liquid Bridge.

11 Mixed Buoyancy–Marangoni Convection.

11.1 The Canonical Problem: The Infinite Horizontal Layer.

11.2 Finite-sized Systems Filled with Liquid Metals.

11.3 Typical Terrestrial Laboratory Experiments with Transparent Liquids.

11.4 The Rectangular Liquid Layer.

11.5 Effects Originating from the Walls.

11.6 The Open Vertical Cavity.

11.7 The Annular Pool.

11.8 The Liquid Bridge on the Ground.

12 Hybrid Regimes with Vibrations.

12.1 RB Convection with Vertical Shaking.

12.2 Complex Order, Quasi-periodic Crystals and Superlattices.

12.3 RB Convection with Horizontal or Oblique Shaking.

12.4 Laterally Heated Systems and Parametric Resonances.

12.5 Control of Thermogravitational Convection.

12.6 Mixed Marangoni–Thermovibrational Convection.

12.7 Modulation of Marangoni–Bénard Convection.

13 Flow Control by Magnetic Fields.

13.1 Static and Uniform Magnetic Fields.

13.2 Historical Developments and Current Status.

13.3 Rotating Magnetic Fields.

13.4 Gradients of Magnetic Fields and Virtual Microgravity.

References.

Index.