Theory and modelling with direct numerical simulation and experimental observations are indispensable in the understanding of the evolution of nature, in this case the theory and modelling of plasma and fluid turbulence. Plasma and Fluid Turbulence: Theory and Modelling explains modelling methodologies in depth with regard to turbulence phenomena and turbulent transport both in fluids and plasmas. Special attention is paid to structural formation and transitions.
In this detailed book, the authors examine the underlying ideas describing turbulence, turbulent transport, and structural transitions in plasmas and fluids. By comparing and contrasting turbulence in fluids and plasmas, they demonstrate the basic physical principles common to fluids and plasmas while also highlighting particular differences. The book also discusses the application of these ideas to neutral fluids.
Part I presents a general introduction to turbulence and structural formation in fluids and plasmas, and Part II explains methodologies for fluid turbulence. In Part III, the authors describe the subjects in magnetohydrodynamics, in particular, dynamo problems. The final section, Part IV, considers plasma turbulence and transport.
Table of Contents
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
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