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Author Shats, Michael.

Title Lecture Notes on Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media : Selected Lectures from the 19th Canberra International Physics Summer School
Published Singapore : World Scientific Publishing Company, 2006
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Description 1 online resource (397 pages)
Series World Scientific Lecture Notes in Complex Systems ; v.4
World Scientific lecture notes in complex systems.
Contents Preface; Contents; Chapter 1. Introduction to Developed Turbulence; 1.1. Introduction; 1.2. Weak wave turbulence; 1.3. Strong wave turbulence; 1.4. Incompressible turbulence; 1.5. Zero modes and anomalous scaling; Bibliography; Chapter 2. Renormalization and Statistical Methods; 2.1. Introduction; 2.2. Overview of renormalization in physics with application to turbulence; 2.2.1. The basic programme of statistical physics; 2.2.2. Theoretical approaches; 2.2.3. Perturbation theory; 2.2.4. Mean-field theories; 2.2.5. Problems with many scales: the renormalization group
2.3. Renormalized perturbation theories and two-point turbulence closures2.3.1. A brief history of closures; 2.3.2. Basic equations in k-space; 2.3.3. Quasi-normality hypothesis; 2.3.4. Perturbation theory; 2.3.5. Quasi-normality versus perturbation theory; 2.3.6. Renormalised perturbation theory (RPT): the general idea; 2.3.7. Assessment of the pioneering RPTs; 2.3.8. The local energy transfer (LET) theory; 2.3.9. Numerical computation of RPTs; 2.3.10. Perceptions of RPTs; 2.3.11. New developments in LET; 2.3.12. Single-time LET equations
2.4. Renormalization group (RG) applied to macroscopic fluid turbulence2.4.1. Three flavours of RG; 2.4.2. RG Algorithm for turbulence; 2.4.3. Turbulence mode elimination: the basic problem; 2.4.4. Gaussian perturbation theory in the limit k ₂!0; 2.4.5. The two-field theory of turbulence; 2.4.6. Update of the two-field theory of turbulence; 2.4.7. Non-Gaussian perturbation theory; 2.5. Conclusion; Bibliography; Chapter 3. Turbulence and Coherent Structures in the Ocean; 3.1. Introduction; 3.2. Specification of the problem; 3.2.1. Governing equations; 3.2.2. The ocean energy balances
3.2.3. A fundamental problem3.3. Energy input; 3.3.1. Surface momentum forcing; 3.3.2. Tidal forcing; 3.3.3. Buoyancy forcing; 3.4. Energetics of mixing; 3.4.1. A simple example; 3.4.2. Stability of stratified shear flows; 3.4.3. Turbulent stratified shear flows; 3.4.4. Mixing associated with the abyssal stratification; 3.5. Energy transformations; 3.5.1. Internal wave pathway; 3.5.2. The meso-scale eddy pathway; 3.6. Summary and conclusions; Chapter 4. Analytical Descriptions of Plasma Turbulence; 4.1. LECTURE 1 -- Introduction to Plasma Turbulence
4.1.1. The Liouville and Klimontovich equations, the Vlasov -- Poisson system, and plasma kinetic equations4.1.2. Basic concepts of linear theory; 4.1.3. The gyrokinetic description; 4.1.4. Drift waves and the Hasegawa-Mima equation; 4.1.5. The gyrokinetic transport problem; 4.1.6. Some other important equations; 4.1.7. The transition to plasma turbulence; 4.2. LECTURE 2 -- Statistical Closures and Plasma Turbulence; 4.2.1. Quasilinear theory; 4.2.2. Weak-turbulence theory; 4.2.3. Resonance-broadening theory; 4.2.4. ""Systematic"" renormalization and the direct-interaction approximation
Summary 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
Notes 4.2.5. Markovian closures
Print version record
Form Electronic book
Author Punzmann, Horst.
ISBN 9789812774071