Mathematical and Physical Theory of Turbulence, Volume 250: 1st Edition (Hardback) book cover

Mathematical and Physical Theory of Turbulence, Volume 250

1st Edition

Edited by John Cannon, Bhimsen Shivamoggi

Chapman and Hall/CRC

208 pages | 46 B/W Illus.

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Description

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.

Reviews

… 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

Table of Contents

A MATHEMATICIAN REFLECTS: BANQUET REMARKS

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

About the Series

Lecture Notes in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
SCI040000
SCIENCE / Mathematical Physics