Lecture Notes on Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media : Selected Lectures from the 19th Canberra International Physics Summer School.

By: Shats, MichaelContributor(s): Punzmann, HorstSeries: World Scientific Lecture Notes in Complex Systems SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2007Copyright date: ©2006Description: 1 online resource (397 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789812774071Subject(s): Turbulence -- Mathematical models -- Congresses.;Hydrodynamics -- CongressesGenre/Form: Electronic books. Additional physical formats: Print version:: Lecture Notes on Turbulence and Coherent Structures in Fluids, Plasmas and Nonlinear Media : Selected Lectures from the 19th Canberra International Physics Summer SchoolDDC classification: 629.132305 LOC classification: QA913 -- .C36 2006ebOnline resources: Click to View
Contents:
Intro -- Contents -- Preface -- 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 closures -- 2.3.1. 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 turbulence -- 2.4.1. 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 → 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 problem -- 3.3. 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 equations -- 4.1.2. 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 -- 4.3. LECTURE 3 - Zonal Flows in Plasmas -- 4.3.1. Modulational instability and zonal-flow generation -- 4.3.2. Zonal flows, the Dimits shift, and the transition to ITG turbulence -- 4.3.3. Spectral bifurcations and the L-H transition -- 4.3.4. Interactions of disparate scales in steady-state turbulence -- 4.3.5. Geodesic acoustic modes -- 4.3.6. Transport due to electron-temperature-gradient driven modes -- 4.4. LECTURE 4 Intermittency and Coherent Structures in Plasmas -- 4.4.1. Definition of intermittency -- 4.4.2. Flux and intermittency -- 4.4.3. Flux-driven transport -- 4.4.4. Blobs -- 4.4.5. Summary and final remarks -- 4.4.6. The last word -- Appendix A. Notation -- Bibliography.
Chapter 5. Experimental Studies of Plasma Turbulence -- 5.1. Introduction -- 5.2. Experimental techniques and diagnostic tools in plasma turbulence -- 5.2.1. Langmuir probes -- 5.2.2. Characterization of turbulent transport using probes -- 5.2.3. Collective (Bragg) scattering of electromagnetic waves by density fluctuations -- 5.2.4. Reflectometry in fluctuation studies -- 5.2.5. Doppler reflectometry -- 5.2.6. Optical imaging of turbulent fluctuations -- 5.2.7. Heavy ion beam probe -- 5.3. Spectral analysis techniques -- 5.3.1. Higher-order spectral analysis -- 5.3.2. Wave coupling equation -- 5.3.3. Computation of the power transfer function -- 5.3.4. Amplitude correlation technique -- 5.4. Experimental evidence of the inverse energy cascade in plasma -- 5.4.1. Applicability of the nonlinear spectral transfer model -- 5.4.2. Results on the spectral transfer analysis -- 5.5. Quasi-two-dimensional turbulence in fluids and plasma and generation of zonal flows -- 5.5.1. Spectral condensation of 2D turbulence -- 5.5.2. Zonal flows in plasma turbulence -- 5.6. Conclusion -- Bibliography -- Chapter 6. The Numerical Computation of Turbulence -- 6.1. The self-similar energy cascade -- 6.1.1. Spectra -- 6.2. Other fractal processes in physics -- 6.3. Inhomogeneity and anisotropy -- 6.3.1. The energy equation -- 6.3.2. The eddy viscosity approximation -- 6.4. Computing turbulence -- 6.5. Direct numerical simulations -- 6.6. Large-eddy simulations -- 6.7. Reynolds-averaged Navier - Stokes simulations -- Bibliography -- Chapter 7. Particle Image Velocimetry - Application to Turbulence Studies -- 7.1. Introduction to laser-based velocimetry and PIV -- 7.2. Principles and characteristics of PIV -- 7.3. Mathematical analysis of cross-correlation of single exposed image pairs -- 7.3.1. Cross-correlation analysis using Gaussian particle image models.
7.4. Spatial resolution -- 7.4.1. The effect of velocity gradients on cross-correlation analysis of single exposed image pairs -- 7.4.2. Effective wavenumber relationships: accuracy of spatial numerical differentiation of PIV measurements -- 7.5. Example of PIV - turbulent round jet -- 7.5.1. Round jet geometry, coordinates and parameters -- 7.5.2. Turbulence scales in turbulent jets: estimated Taylor and Kolmogorov micro-scales -- 7.5.3. Issues with spatial resolution: velocity measurement -- 7.6. Concluding remarks -- Bibliography -- Chapter 8. Vortex Flows in Optical Fields -- 8.1. Introduction -- 8.2. Vortices in coherent and partially-coherent light waves -- 8.3. Self-trapped vortex beams in nonlinear optical media -- 8.3.1. Bright vortex solitons -- 8.3.2. Modulational instability -- 8.3.3. Azimuthons -- 8.4. Discrete vortices -- 8.5. Vortices in lasers and optical turbulence -- 8.6. Conclusions and Outlook -- Bibliography.
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, 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.
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Intro -- Contents -- Preface -- 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 closures -- 2.3.1. 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 turbulence -- 2.4.1. 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 → 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 problem -- 3.3. 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 equations -- 4.1.2. 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 -- 4.3. LECTURE 3 - Zonal Flows in Plasmas -- 4.3.1. Modulational instability and zonal-flow generation -- 4.3.2. Zonal flows, the Dimits shift, and the transition to ITG turbulence -- 4.3.3. Spectral bifurcations and the L-H transition -- 4.3.4. Interactions of disparate scales in steady-state turbulence -- 4.3.5. Geodesic acoustic modes -- 4.3.6. Transport due to electron-temperature-gradient driven modes -- 4.4. LECTURE 4 Intermittency and Coherent Structures in Plasmas -- 4.4.1. Definition of intermittency -- 4.4.2. Flux and intermittency -- 4.4.3. Flux-driven transport -- 4.4.4. Blobs -- 4.4.5. Summary and final remarks -- 4.4.6. The last word -- Appendix A. Notation -- Bibliography.

Chapter 5. Experimental Studies of Plasma Turbulence -- 5.1. Introduction -- 5.2. Experimental techniques and diagnostic tools in plasma turbulence -- 5.2.1. Langmuir probes -- 5.2.2. Characterization of turbulent transport using probes -- 5.2.3. Collective (Bragg) scattering of electromagnetic waves by density fluctuations -- 5.2.4. Reflectometry in fluctuation studies -- 5.2.5. Doppler reflectometry -- 5.2.6. Optical imaging of turbulent fluctuations -- 5.2.7. Heavy ion beam probe -- 5.3. Spectral analysis techniques -- 5.3.1. Higher-order spectral analysis -- 5.3.2. Wave coupling equation -- 5.3.3. Computation of the power transfer function -- 5.3.4. Amplitude correlation technique -- 5.4. Experimental evidence of the inverse energy cascade in plasma -- 5.4.1. Applicability of the nonlinear spectral transfer model -- 5.4.2. Results on the spectral transfer analysis -- 5.5. Quasi-two-dimensional turbulence in fluids and plasma and generation of zonal flows -- 5.5.1. Spectral condensation of 2D turbulence -- 5.5.2. Zonal flows in plasma turbulence -- 5.6. Conclusion -- Bibliography -- Chapter 6. The Numerical Computation of Turbulence -- 6.1. The self-similar energy cascade -- 6.1.1. Spectra -- 6.2. Other fractal processes in physics -- 6.3. Inhomogeneity and anisotropy -- 6.3.1. The energy equation -- 6.3.2. The eddy viscosity approximation -- 6.4. Computing turbulence -- 6.5. Direct numerical simulations -- 6.6. Large-eddy simulations -- 6.7. Reynolds-averaged Navier - Stokes simulations -- Bibliography -- Chapter 7. Particle Image Velocimetry - Application to Turbulence Studies -- 7.1. Introduction to laser-based velocimetry and PIV -- 7.2. Principles and characteristics of PIV -- 7.3. Mathematical analysis of cross-correlation of single exposed image pairs -- 7.3.1. Cross-correlation analysis using Gaussian particle image models.

7.4. Spatial resolution -- 7.4.1. The effect of velocity gradients on cross-correlation analysis of single exposed image pairs -- 7.4.2. Effective wavenumber relationships: accuracy of spatial numerical differentiation of PIV measurements -- 7.5. Example of PIV - turbulent round jet -- 7.5.1. Round jet geometry, coordinates and parameters -- 7.5.2. Turbulence scales in turbulent jets: estimated Taylor and Kolmogorov micro-scales -- 7.5.3. Issues with spatial resolution: velocity measurement -- 7.6. Concluding remarks -- Bibliography -- Chapter 8. Vortex Flows in Optical Fields -- 8.1. Introduction -- 8.2. Vortices in coherent and partially-coherent light waves -- 8.3. Self-trapped vortex beams in nonlinear optical media -- 8.3.1. Bright vortex solitons -- 8.3.2. Modulational instability -- 8.3.3. Azimuthons -- 8.4. Discrete vortices -- 8.5. Vortices in lasers and optical turbulence -- 8.6. Conclusions and Outlook -- Bibliography.

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.

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