1st Edition
Mathematical and Physical Theory of Turbulence, Volume 250
Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence.
Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier–Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities and inviscid dissipation energy; validity of the idealized model incorporating local isotropy, homogeneity, and universality of small scales of high Reynolds numbers, Lagrangian statistics, and measurements; and subrigid-scale modeling and hybrid methods involving a mix of Reynolds-averaged Navier–Stokes (RANS), large-eddy simulations (LES), and direct numerical simulations (DNS).
By sharing their expertise and recent research results, the authoritative contributors in Mathematical and Physical Theory of Turbulence promote further advances in the field, benefiting applied mathematicians, physicists, and engineers involved in understanding the complex issues of the turbulence problem.
Alan Turing
Henry Whitehead
Jean-Pierre Serre
Epilogue
LAGRANGIAN DESCRIPTION OF TURBULENCE
Introduction
Particles in Fluid Turbulence
Unforced Evolution of Passive Fields
Cascades of a Passive Tracer
Active Tracers
Conclusion
Acknowledgment
References
TWO-DIMENSIONAL TURBULENCE AN OVERVIEW
Introduction
Conservation Laws and Cascades
Markovian Closure
Numerical Simulations: The Decay Problem
A New Scaling Theory for Turbulent Decay
A New Dynamic Model for Turbulent Decay
Forced Two-Dimensional Turbulence
A Question of End States
Flow over Topography
Effects of β
Concluding Remarks
Acknowledgments
References
STATISTICAL PLASMA PHYSICS IN A STRONG MAGNETIC FIELD: PARADIGMS AND PROBLEMS
Introduction
Introductory Plasma-Physics Background, Particularly Gyrokinetics
Plasma Applications of Statistical Methods
Statistical Description of Long-Wavelength Flows
Discussion
Acknowledgments
References
SOME REMARKS ON DECAYING TWO-DIMENSIONAL TURBULENCE
Introduction
The Statistical Mechanics of Vorticity
Numerical Results: Rectangular Periodic Boundaries
Numerical Results: Material Boundaries
Pressure Determinations and Their Ambiguities
Summary
Acknowledgment
References
STATISTICAL AND DYNAMICAL QUESTIONS IN STRATIFIED TURBULENCE
Isotropic Turbulence and Resolution Issues at Large Scales
Stably Stratified Turbulence
Concluding Comments
References
WAVELET SCALING AND NAVIER–STOKES REGULARITY
Background
Navier–Stokes in Wavelet Space
Isolated Singularities and Scaling of Wavelet Coefficients Evolution of Singularities
Discussion
References
GENERALIZATION OF THE EDDY VISCOSITY MODEL — APPLICATION TO A TEMPERATURE SPECTRUM
Introduction
Eddy Viscosity Model
Application to a Temperature Spectrum
Conclusions
References
CONTINUOUS MODELS FOR THE SIMULATION OF TURBULENT FLOWS: AN OVERVIEW AND ANALYSIS
Introduction
Development of Continuous RANS-LES Models— Possible Bases
DNS of Kolmogorov Flow
Continuous RANS-LES Model Development and Application
Summary and Conclusions
Acknowledgments
References
ANALYTICAL USES OF WAVELETS FOR NAVIER–STOKES TURBULENCE
Background
Eliminating Pressure
Filtered Flexion and Wavelet Transforms
Applications
Conclusion
References
TIME AVERAGING, HIERARCHY OF THE GOVERNING EQUATIONS, AND THE BALANCE OF TURBULENT KINETIC ENERGY
Introduction
Various Notions of Time Averaging
Governing Equations
Constitutive and Closure Theories
Turbulent Kinetic Energy
Acknowledgments
References
THE ROLE OF ANGULAR MOMENTUM INVARIANTS IN HOMOGENEOUS TURBULENCE
Introduction
Loitsyansky’s Integral for Isotropic Turbulence
Kolmogorov’s Decay Laws in Isotropic Turbulence
Landau’s Angular Momentum in Isotropic Turbulence
Long-Range Correlations in Homogenous Turbulence
The Growth of Anisotropy in MHD Turbulence
The Landau Invariant for Homogeneous MHD Turbulence
Decay Laws at Low Magnetic Reynolds Number
A Loitsyansky-type Invariant for Stratified Turbulence
Conclusions
References
ON THE NEW CONCEPT OF TURBULENCE MODELING IN FULLY DEVELOPED TURBULENT CHANNEL FLOW AND BOUNDARY LAYER
Introduction
Eddy Viscosity Turbulence Modeling
New Concept of Turbulence Modeling
Results and Discussion
Conclusions
Acknowledgments
References
Biography
John Cannon, Bhimsen Shivamoggi
… this is a welcome book posing interesting questions concerning the development of turbulence theory and computations in 2D and 3D for many essential industrial and environmental issues, which should be read by any researcher interested in this important topic.
—Marcel Lesieur (French Academy of Sciences and Grenoble Institute of Technology), Theoretical and Computational Fluid Dynamics, Vol. 22, 2008
