Lecture notes on turbulence and coherent structures in fluids, plasmas and nonlinear media [[electronic resource] /] / editors, Michael Shats, Horst Punzmann

• Record Nr.: UNINA9910782307903321
• Pubbl/distr/stampa: Singapore ; ; Hackensack, NJ, : World Scientific, c2006
• ISBN: 1-281-91926-8; 9786611919269; 981-277-407-6
• Descrizione fisica: 1 online resource (397 p.)
• Collana: World Scientific lecture notes in complex systems ; ; v. 4
• Altri autori (Persone): ShatsMichael; PunzmannHorst
• Disciplina: 530.42
• Soggetti: Turbulence - Mathematical models; Hydrodynamics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "This book is based on lectures delivered at the 19th Canberra International Physics Summer School held at the Australian National University in Canberra (Australia) from 16-20 January 2006."--P. v.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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; 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; 4.2.5. Markovian closures
• Sommario/riassunto: 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,