Thermal Convection – Patterns, Stages of Evolution and Stability PATTERNS, EVOLUTION AND STABILITY

Thermal Convection - Patterns, Stages of Evolution and Stability Behavior provides the reader with an ensemble picture of the subject, illustrating the state-of-the-art and providing the researchers from universities and industry with a basis on which they are able to estimate the possible impact of a variety of parameters. Unlike earlier books on the subject, the heavy mathematical background underlying and governing the behaviors illustrated in the text are kept to a minimum. The text clarifies some still unresolved controversies pertaining to the physical nature of the dominating driving force responsible for asymmetric/oscillatory convection in various natural phenomena and/or technologically important processes and can help researchers in elaborating and validating new, more complex models, in accelerating the current trend towards predictable and reproducible natural phenomena and in establishing an adequate scientific foundation to industrial processes. Thermal Convection - Patterns, Stages of Evolution and Stability Behavior is intended as a useful reference guide for specialists in disciplines such as the metallurgy and foundry field and researchers and scientists who are now coordinating their efforts to improve the quality of semiconductor or macromolecular crystals. The text may also be of use to organic chemists and materials scientists, atmosphere and planetary physicists, as well as an advanced level text for students taking part in courses on the physics of fluids, fluid mechanics, the behavior and evolution of non-linear systems, environmental phenomena and materials engineering.

Preface Acknowledgements CHAPTER 1 Equations, General concepts and Methods of Analysis 1.1 Pattern Formation and Nonlinear Dynamics 1.2 The Navier-Stokes Equations 1.3 The 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 CHAPTER 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 CHAPTER 3 Examples of Thermal Fluid Convection and Pattern Formation in Nature and Technology 3.1 Technological processes: Small scale laboratory and industrial set-ups 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 CHAPTER 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 Twodimensional models 4.9 Threedimensional parellelepipedic 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 ChaosProblem 4.13 Threedimensional Convection in a Spherical Shell CHAPTER 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 CHAPTER 6 Systems heated from the side: The Hadley Flow 6.1 The Infinite Horizontal Layer 6.2 Twodimensional horizontal enclosures 6.3 The infinite vertical layer: Cats-eye Patterns and temperature Waves 6.4 Threedimensional parallelepipedic enclosures 6.5 Cylindrical geometries CHAPTER 7 Thermogravitational Convection in Inclined Systems 7.1 Inclined Layer Convection 7.2 Inclinedside-heated slots CHAPTER 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 CHAPTER 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 induced by the lateral confinement 9.5 Temperature Gradient Inclination CHAPTER 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 CHAPTER 11 Mixed Buoyancy-Marangoni Convection 11.1 The Canonical Problem: the infinite horizontal layer 11.2 Finite-size 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 CHAPTER 12 Hybrid Regimes with Vibrations 12.1 RB Convection with Vertical Shaking 12.2 Complex Order, Quasiperiodic 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 CHAPTER 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