Lecture Notes On Turbulence

This book is a formal presentation of lectures given at the 1987 Summer School on Turbulence, held at the National Center for Atmospheric Research under the auspices of the Geophysical Turbulence Program. The lectures present in detail certain of the more challenging and interesting current turbulence research problems in engineering, meteorology, plasma physics, and mathematics. The lecturers-Uriel Frisch (Mathematics), Douglas Lilly (Meteorology), David Montgomery (Plasma Physics), and Hendrik Tennekes (Engineering) — are distinguished for both their research contributions and their abilities to communicate these to students with enthusiasm. This book is distinguished by its simultaneous focus on the fundamentals of turbulent flows (in neutral and ionized fluids) and on a presentation of current research tools and topics in these fields. Contents:Two- and Three-Dimensional Turbulence (H Tennekes)Magnetohydrodynamic Turbulence (D Montgomery)Helicity (D Lilly)Lectures on Turbulence and Lattice Gas Hydrodynamics (U Frisch) Readership: Serious students (ranging from graduate students to post-doctoral researchers) of fluid and MHD turbulence, and those interested in learning in some depth about challenging problems in these fields. Keywords:Turbulence;Geophysical Turbulence;Meteorological Turbulence;Plasma Turbulence;Magnetohydrodynamic Turbulence;Theory of Turbulence;Cellular AutomataReview: “… a record of some stimulating and informative lectures.” Journal of Fluid Mechanics “… give a good grasp of many questions of importance in this essential field.” Monatshefte für Mathematik

This book is based on the lectures delivered at the 19th Canberra International Physics Summer School held at the Australian National University in Canberra (Australia) in January 2006.The problem of turbulence and coherent structures is of key importance in many fields of science and engineering. It is an area which is vigorously researched across a diverse range of disciplines such as theoretical physics, oceanography, atmospheric science, magnetically confined plasma, nonlinear optics, etc. Modern studies in turbulence and coherent structures are based on a variety of theoretical concepts, numerical simulation techniques and experimental methods, which cannot be reviewed effectively by a single expert.The main goal of these lecture notes is to introduce state-of-the-art turbulence research in a variety of approaches (theoretical, numerical simulations and experiments) and applications (fluids, plasmas, geophysics, nonlinear optical media) by several experts. A smooth introduction is presented to readers who are not familiar with the field, while reviewing the most recent advances in the area. This collection of lectures will provide a useful review for both postgraduate students and researchers new to the advancements in this field, as well as specialists seeking to expand their knowledge across different areas of turbulence research.

This book is a formal presentation of lectures given at the 1987 Summer School on Turbulence, held at the National Center for Atmospheric Research under the auspices of the Geophysical Turbulence Program. The lectures present in detail certain of the more challenging and interesting current turbulence research problems in engineering, meteorology, plasma physics, and mathematics. The lecturers-Uriel Frisch (Mathematics), Douglas Lilly (Meteorology), David Montgomery (Plasma Physics), and Hendrik Tennekes (Engineering) ? are distinguished for both their research contributions and their abilities to communicate these to students with enthusiasm. This book is distinguished by its simultaneous focus on the fundamentals of turbulent flows (in neutral and ionized fluids) and on a presentation of current research tools and topics in these fields.

Two- and three-dimensional turbulence by Hendrik Tennekes. Preface. ch. 1. Introduction. ch. 2. Vorticity dynamics. ch. 3. The phenomenology of turbulence. ch. 4. Consequences of the Kolmogorov theory. ch. 5. Predictability and other problems. ch. 6. Predictability of a simple system. ch. 7. Self-consistent scaling in the K - E model. ch. 8. The decay of turbulence in plane homogeneous Shear flow. ch. 9. Second-order modeling : some examples. ch. 10. Part I. Second-order modeling : the surface layer. ch. 11. Part II. Flux maintenance in two-dimensional turbulence -- Magnetohydrodynamic turbulence by David Montgomery. Preface. ch. 1. Magnetofluid turbulence. ch. 2. The origin of turbulence. Part I : Shear flow and current gradients. ch. 2. (continued) the origin of turbulence. Part II : MHD analogue. ch. 3. Ideal MHD stability, incompressibiity conditions, and ideal invariants. ch. 4. Some connections with statistical mechanics. ch. 5. More statistical mechanics. ch. 6. Spectral cascades and turbulent relaxation processes. ch. 7. Anisotropic effects in MHD. ch. 8. Compressible MHD turbulent relaxation. ch. 9. Part I: MHD turbulence in reversed-field pinch plasmas. ch. 9. (continued) Part II. 3D reversed-field pinch simulation. ch. 10. MHD (plasma) turbulence to the year 2000 -- Lecture notes by Douglas Lilly. Preface. ch. 1. Helicity. ch. 2. Helical convection. ch. 3. Flow fields in helical convection. ch. 4. Turbulence in stably stratified fluids. ch. 5. Modes of turbulence in stably stratified environments : part I. ch. 6. Modes of turbulence in stably stratified environments : part II. ch. 7. Subgrid closures in large eddy simulation : part I. ch. 8. Subgrid closures in large eddy simulation : part II -- Lectures on turbulence and lattice gas hydrodynamics by Uriel Frisch. Preface. ch. 1. Current beliefs about fully developed turbulence : part I. ch. 2. Current beliefs about fully developed turbulence : part II. ch. 3. Turbulent transport of scalars and magnetic fields. ch. 4. Large-scale instability in 3d flows lacking parity-invariance. ch. 5. Lattice gas hydrodynamics : introduction. ch. 6. Lattice gas hydrodynamics : microdynamics. ch. 7. Lattice gas hydrodynamics : collisions and equilibria. ch. 8. Lattice gas hydrodynamics : from microdynamics to the Navier-Stokes equations. ch. 9. Lattice gas hydrodynamics : Reynolds number, noisy hydrodynamics. ch. 10. Lattice gas hydrodynamics : software and hardware implementations. Concluding remarks. ch. 11. Large-scale flow driven by the anisotropic kinetic alpha effect

This book is based on the lectures delivered at the 19th Canberra International Physics Summer School held at the Australian National University in Canberra (Australia) in January 2006.The problem of turbulence and coherent structures is of key importance in many fields of science and engineering. It is an area which is vigorously researched across a diverse range of disciplines such as theoretical physics, oceanography, atmospheric science, magnetically confined plasma, nonlinear optics, etc. Modern studies in turbulence and coherent structures are based on a variety of theoretical concepts, numerical simulation techniques and experimental methods, which cannot be reviewed effectively by a single expert.The main goal of these lecture notes is to introduce state-of-the-art turbulence research in a variety of approaches (theoretical, numerical simulations and experiments) and applications (fluids, plasmas, geophysics, nonlinear optical media) by several experts. A smooth introduction is presented to readers who are not familiar with the field, while reviewing the most recent advances in the area. This collection of lectures will provide a useful review for both postgraduate students and researchers new to the advancements in this field, as well as specialists seeking to expand their knowledge across different areas of turbulence research.

This book is based on the lectures delivered at the 19th Canberra International Physics Summer School held at the Australian National University in Canberra (Australia) in January 2006.The problem of turbulence and coherent structures is of key importance in many fields of science and engineering. It is an area which is vigorously researched across a diverse range of disciplines such as theoretical physics, oceanography, atmospheric science, magnetically confined plasma, nonlinear optics, etc. Modern studies in turbulence and coherent structures are based on a variety of theoretical concepts, numerical simulation techniques and experimental methods, which cannot be reviewed effectively by a single expert.The main goal of these lecture notes is to introduce state-of-the-art turbulence research in a variety of approaches (theoretical, numerical simulations and experiments) and applications (fluids, plasmas, geophysics, nonlinear optical media) by several experts. A smooth introduction is presented to readers who are not familiar with the field, while reviewing the most recent advances in the area. This collection of lectures will provide a useful review for both postgraduate students and researchers new to the advancements in this field, as well as specialists seeking to expand their knowledge across different areas of turbulence research.

Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.

This textbook is based on the lectures on turbulence given in the Masters programme at Universit Pierre et Marie Curie and Ecole Polytechnique. The book covers the classic topics on turbulence that includes: introduction to fundamentals of statistical and spectral analysis, dimensional analysis, Kolmogorov theory and energy cascade, the hierarchy of turbulent flows ranging from isotropic turbulence to non-homogeneous shear flows, and extension to compressible turbulence illuminated using Kovasznay model decomposition. A substantial section of this volume is devoted to exercises and problems to guide readers through the book in applying the theories learnt to the problems provided. Furthermore, all-important exercises and problems are first presented in the usual short "workout" fashion, followed by the full solution to demonstrate the process. Turbulence is a multidisciplinary subject that cut across engineering and earth sciences; covering areas such as pollution control, global warming and acoustic pollution. Therefore, in all chapters, the usual Navier Stokes equations supplemented with a passive scalar equation will be used to serve as a simplified model for pollutant or temperature, intended to give readers a comprehensive view of turbulent scalar field dynamics. Lecture Notes on Turbulence: Problems and Solutions provides readers with a comprehensive introduction to turbulence dynamics and modelling, and will be of interest to Masters students, PhD students and experienced professionals who wish to get an insight into the field of turbulence.