Rotating Thermal Flows in Natural and Industrial Processes

Rotating Thermal Flows in Natural and Industrial Processes provides the reader with a systematic description of the different types of thermal convection and flow instabilities in rotating systems, as present in materials, crystal growth, thermal engineering, meteorology, oceanography, geophysics and astrophysics. It expressly shows how the isomorphism between small and large scale phenomena becomes beneficial to the definition and ensuing development of an integrated comprehensive framework. This allows the reader to understand and assimilate the underlying, quintessential mechanisms without requiring familiarity with specific literature on the subject.

Topics treated in the first part of the book include:

• Thermogravitational convection in rotating fluids (from laminar to turbulent states);

• Stably stratified and unstratified shear flows;

• Barotropic and baroclinic instabilities;

• Rossby waves and Centrifugally-driven convection;

• Potential Vorticity, Quasi-Geostrophic Theory and related theorems;

• The dynamics of interacting vortices, interacting waves and mixed (hybrid) vortex-wave states;

• Geostrophic Turbulence and planetary patterns.

The second part is entirely devoted to phenomena of practical interest, i.e. subjects relevant to the realms of industry and technology, among them:

• Surface-tension-driven convection in rotating fluids;

• Differential-rotation-driven (forced) flows;

• Crystal Growth from the melt of oxide or semiconductor materials;

• Directional solidification;

• Rotating Machinery;

• Flow control by Rotating magnetic fields;

• Angular Vibrations and Rocking motions;

Covering a truly prodigious range of scales, from atmospheric and oceanic processes and fluid motion in "other solar-system bodies", to convection in its myriad manifestations in a variety of applications of technological relevance, this unifying text is an ideal reference for physicists and engineers, as well as an important resource for advanced students taking courses on the physics of fluids, fluid mechanics, thermal, mechanical and materials engineering, environmental phenomena, meteorology and geophysics.

Autorentext

Dr Marcello Lappa received his M.Sc. and Ph.D. in Aerospace Engineering from the University of Naples "Federico II", Italy. He spent time as a post-doc at the University of Naples as well as at the Institute of Advanced Material Study, Fukuoka, Kyushu University in Japan. From 2002-2008 he was a Senior Researcher at the Microgravity Advanced Research and Support Center (MARS). From 2005-present he has served as Editor-in-chief of the International Scientific Journal Fluid Dynamics & Materials Processing.
His research interests include: Buoyant flows; Thermocapillary (Marangoni) flows; Materials Processing CFD; Control of flow patterns and their stability; Multi phase flows; Methods of numerical analysis in Computational Fluid; Dynamics and Heat/Mass Transfer; High Performance Computing; Biological fluid dynamics; Tissue Engineering and CFD.

Inhalt
Preface xiii

Acknowledgements xvii

1 Equations, General Concepts and Nondimensional Numbers 1

1.1 The Navier-Stokes and Energy Equations 1

1.1.1 The Continuity Equation 2

1.1.2 The Momentum Equation 2

1.1.3 The Total Energy Equation 2

1.1.4 The Budget of Internal Energy 3

1.1.5 Closure Models 3

1.2 Some Considerations about the Dynamics of Vorticity 5

1.2.1 Vorticity and Circulation 5

1.2.2 Vorticity in Two Dimensions 7

1.2.3 Vorticity Over a Spherical Surface 8

1.2.4 The Curl of the Momentum Equation 10

1.3 Incompressible Formulation 10

1.4 Buoyancy Convection 13

1.4.1 The Boussinesq Model 13

1.4.2 The Grashof and Rayleigh Numbers 14

1.5 Surface-Tension-Driven Flows 14

1.5.1 Stress Balance 15

1.5.2 The Reynolds and Marangoni Numbers 16

1.5.3 The Microgravity Environment 18

1.6 Rotating Systems: The Coriolis and Centrifugal Forces 19

1.6.1 Generalized Gravity 20

1.6.2 The Coriolis, Taylor and Rossby Numbers 21

1.6.3 The Geostrophic Flow Approximation 22

1.6.4 The TaylorProudman Theorem 23

1.6.5 Centrifugal and Stratification Effects: The Froude Number 23

1.6.6 The Rossby Deformation Radius 24

1.7 Some Elementary Effects due to Rotation 25

1.7.1 The Origin of Cyclonic and Anticyclonic flows 25

1.7.2 The Ekman Layer 26

1.7.3 Ekman Spiral 28

1.7.4 Ekman Pumping 28

1.7.5 The Stewartson Layer 30

2 Rayleigh-Benard Convection with Rotation 33

2.1 Rayleigh-Benard Convection with Rotation in Infinite Layers 34

2.1.1 Linear Stability Analysis 35

2.1.2 Asymptotic Analysis 36

2.2 The Kuppers-Lortz Instability and Domain Chaos 38

2.3 Patterns with Squares 41

2.4 Typical Phenomena for Pr=

2.4.1 Spiral Defect Chaos and Chiral Symmetry 42

2.4.2 The Interplay between the Busse Balloon and the KL Instability 45

2.5 The Low-Pr Hopf Bifurcation and Mixed States 48

2.5.1 Standing and Travelling Rolls 50

2.5.2 Patterns with the Symmetry of Square and Hexagonal Lattices 52

2.5.3 Other Asymptotic Analyses 55

2.5.4 Nature and Topology of the Bifurcation Lines in the Space of Parameters (Pr) 56

2.6 Laterally Confined Convection 58

2.6.1 The First Bifurcation and Wall Modes 60

2.6.2 The Second Bifurcation and Bulk Convection 63

2.6.3 Square Patterns Driven by Nonlinear Interactions between Bulk and Wall Modes 64

2.6.4 Square Patterns as a Nonlinear Combination of Bulk Fourier Eigenmodes 67

2.6.5 Higher-Order Bifurcations 69

2.7 Centrifugal Effects 71

2.7.1 Stably Thermally Stratified Systems 71

2.7.2 Interacting Thermogravitational and Centrifugally Driven Flows 74

2.7.3 The Effect of the Centrifugal Force on Domain Chaos 84

2.8 Turbulent Rotating RB Convection 86

2.8.1 The Origin of the Large-scale Circulation 87

2.8.2 Rotating Vortical Plumes 89

2.8.3 Classification of Flow Regimes 91

2.8.4 Suppression of Large-scale Flow and Heat Transfer Enhancement 98

2.8.5 Prandtl Number Effects 102

3 Spherical Shells, Rossby Waves and Centrifugally Driven Thermal Convection 107

3.1 The Coriolis Effect in Atmosphere Dynamics 107

3.1.1 The Origin of the Zonal Winds 107

3.1.2 The Rossby Waves 110

3.2 Self-Gravitating Rotating Spherical Shells 114

3.2.1 Columnar Convective Patterns 115

3.2.2 A Mechanism for Generating Differential Rotation 119

3.2.3 Higher-Order Modes of Convection 121

3.2.4 Equatorially Attached Modes of Convection 126

3.2.5 Polar Convection 127

3.3 Centrifugally Driven Thermal Convection 128

4 The Baroclinic Problem 135 4.1 Energetics of Convection and Heuristic Arg...