Interdisciplinary Aspects of Turbulence (eBook)

Wolfgang Hillebrandt is member of the Editorial Board of LNP and Director Max-Planck-Institute for Astrophysics. He is one of the leading figures in simulations of supernova explosions.

Preface 6
An Introduction to Turbulence 11
The Fundamentals of Turbulence 12
Statistics and Simulations of Turbulent Flows 21
Summary 26
References 29
Nonextensive Statistical Mechanics and Nonlinear Dynamics 31
Introduction 31
Extensivity of the (Nonadditive) Entropy Sq 36
Entropy Production Per Unit Time for Sq 40
Superstatistics and Connection With Turbulence 45
Conclusions 52
References 53
Turbulent Convection and Numerical Simulations in Solar and Stellar Astrophysics 59
Convective Heat Transport and Mixing in Stars 60
Turbulence in the Solar and in Stellar Convection Zones 70
Modelling and Simulating Stellar Turbulent Convection 80
Realistic Simulations of Stellar Convection 88
Boundary Conditions and Reynolds Averages 98
Scaling Relations and Mixing in Overshooting Layers 105
Conclusions 108
References 110
Turbulence in Astrophysical and Geophysical Flows 116
General Considerations 116
The Heisenberg--Kolmogorov Energy Spectrum 120
Heat Fluxes: Local and Non-Local Models 121
Overshooting Regions, OV 126
Semi-Convection and Salt-Fingers: Double Diffusion (DD) Processes 129
OV and DD 132
Effect of Rotation on DD and the OV 132
The Extent of the OV Region 133
Transport of Angular Momentum: The 7 Li Problem 133
Reynolds Stress Model: Buoyancy Only 135
Non-locality: Third-Order Moments 137
Plumes and Turbulence 144
New Plume Model 146
The Morton--Turner--Taylor Plume Model 147
Compressibility and Magnetic Fields 149
Helioseismology 150
Reynolds Stress Model: Buoyancy and Shear 150
Mixing in the Ocean: Mixed layer, Gravity Waves and Tides 153
Mixing in the Ocean: Deep Convection 157
Dissipation: An Open Problem 160
Conclusions 164
References 164
Turbulence in the Lower Troposphere: Second-Order Closure and Mass--Flux Modelling Frameworks 170
Introduction 170
Turbulence Parameterisation Schemes 174
Mass--Flux Convection Schemes 198
Towards a Unified Description of Boundary-Layer Turbulence and Shallow Convection 211
Conclusions 217
References 218
Magnetohydrodynamic Turbulence 231
Introduction 231
Macroscopic Properties 233
Small-Scale Dynamics 238
Spatial Structure 252
Summary 257
References 258
Turbulent Combustion in Thermonuclear Supernovae 263
Introduction 263
Combustion in SNe Ia 265
Modelling Approach 273
Numerical Simulations 285
Conclusion 291
References 293
One-Dimensional Turbulence Stochastic Simulation of Multi-Scale Dynamics 298
A New Modelling Paradigm 298
Implications for Turbulent Flow Modelling 301
Proposed Modelling Strategy 309
Map-Based Advection Models 320
ODT Formulation of Substructure Advancement 323
ODTLES 331
Illustrative ODT Applications 334
Discussion 337
References 338
Index 341