Plasma and Fluid Turbulence

Akira Yoshizawa Institute of Industrial Science, University of Tokyo, Japan Sanae-I Itoh Research Institute for Applied Mechanics, Kyushu University, Japan Kimitaka Itoh National Institute for Fusion Science, Toki, Japan

• Preface, Acknowledgments, PART I GENERAL INTRODUCTION, 1 Introductory Remarks, 2 Structure Formation in Fluids and Plasmas, 2.1 Flow in a Pipe, 2.1.1 Enhancement of Mixing Effects Due to Turbulence, 2.1.2 Mean-Flow Structure Formation in Pipe Flows, 2.2 Magnetic-Field Generation by Turbulent Motion, 2.3 Collimation of Jets, 2.4 Magnetic Confinement of Plasmas, 2.4.1 Magnetic Confinement and Toroidal Plasmas, 2.4.2 Flows in Toroidal Plasmas, 2.4.3 Topological Change of Magnetic Surfaces, 2.5 Nonlinearity in Transport and Structural Transition, 2.5.1 Nonlinear Gradient–Flux Relation, 2.5.2 Bifurcation in Flow, 2.5.3 Bifurcation in Structural Formation, References, PART II FLUID TURBULENCE, Nomenclature, 3 Fundamentals of Fluid Turbulence, 3.1 Fundamental Equations, 3.2 Averaging Procedures, 3.3 Ensemble-Mean Equations, 3.3.1 Mean-Field Equations, 3.3.2 Turbulence Equations, 3.4 Homogeneous Turbulence, 3.4.1 Fundamental Concepts, 3.4.2 Kolmogorov’s Scaling Law, 3.4.3 Failure of Kolmogorov’s Scaling, 3.4.4 Two-Dimensional Turbulence, 3.5 Production and Diffusion Characteristics of Turbulent Energy, References, 4 Heuristic Turbulence Modelling, 4.1 Approaches to Turbulence, 4.2 Algebraic Turbulence Modelling, 4.2.1 Modelling of Reynolds Stress, 4.2.2 Modelling of Heat Flux, 4.2.3 Modelling of Turbulence Equations, 4.2.4 The Simplest Algebraic Model, 4.2.5 Investigation into Some Representative Turbulent Flows, 4.3 Second-Order Modelling, 4.3.1 Modelling of Pressure–Strain Term, 4.3.2 Modelling of Dissipation and Transport Terms, 4.3.3 The Simplest Second-Order Model and its Relationship with a Higher-Order Algebraic Model, 4.4 A Variational-Method Model, 4.4.1 Helicity and Vortical-Structure Persistence, 4.4.2 Derivation of the Vorticity Equation Using the Variational Method, 4.4.3 Analysis of Swirling Pipe Flow, 4.4.4 Swirl Effect on Reynolds Stress, 4.5 Subgrid-Scale Modelling, 4.5.1 Filtering Procedure, 4.5.2 Filtered Equations, 4.5.3 Fixed-Parameter Modelling, 4.5.4