Mathematical and Physical Theory of Turbulence, Volume 250

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ISBN: 9780824723231 | 0824723236
Cover: Hardcover
Copyright: 6/15/2006

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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.

Chapter 1 A Mathematician Reflects: Banquet Remarks

Peter Hilton

1.1 Alan Turing

(1)

1.2 Henry Whitehead

(1)

1.3 Jean-Pierre Serre

(1)

1.4 Epilogue

(3)

Chapter 2 Lagrangian Description of Turbulence

(40)

Gregory Falkovich

2.1 Introduction

(2)

2.1.1 Propagators

(1)

2.1.2 Kraichnan Model

(1)

2.1.3 Large Deviation Approach

(1)

2.2 Particles in Fluid Turbulence

(15)

2.2.1 Single-Particle Diffusion

(1)

2.2.2 Two-Particle Dispersion in a Spatially Smooth Velocity

(3)

2.2.3 Two-Particle Dispersion in a Nonsmooth Incompressible Flow

(3)

2.2.4 Two-Particle Dispersion in a Compressible Flow

(2)

2.2.5 Multiparticle Configurations and Zero Modes

(5)

2.3 Unforced Evolution of Passive Fields

(6)

2.3.1 Decay of Tracer Fluctuations

(4)

2.3.1.1 Smooth Velocity

(1)

2.3.1.2 Nonsmooth Velocity

(1)

2.3.1.3 Scalar Decay with Viscous and Inertial Intervals Present

(1)

2.3.1.4 Scalar Decay in a Finite Box

(1)

2.3.2 Growth of Density Fluctuations in Compressible Flow

(1)

2.3.3 Vector Fields in a Smooth Velocity

(1)

2.3.3.1 Gradients of the Passive Scalar

(1)

2.3.3.2 Small-Scale Magnetic Dynamo

(1)

2.4 Cascades of a Passive Tracer

(6)

2.4.1 Direct Cascade

(5)

2.4.1.1 Direct Cascade in a Smooth Velocity

(1)

2.4.1.2 Anomalies of Tracer Statistics in a Nonsmooth Velocity

(3)

2.4.2 Inverse Cascade in a Compressible Flow

(1)

2.5 Active Tracers

(5)

2.5.1 Activity Changing Cascade Direction

(3)

2.5.1.1 Burgers Turbulence

(2)

2.5.1.2 Two-Dimensional Magnetohydrodynamics

(1)

2.5.2 Two-Dimensional Incompressible Turbulence

(8)

2.5.2.1 Direct Vorticity Cascade in Two Dimensions

(1)

2.5.2.2 Inverse Energy Cascade in Two Dimensions

(1)

2.6 Conclusion

(1)

Acknowledgment

(1)

References

(4)

Chapter 3 Two-Dimensional Turbulence: An Overview

(22)

George F. Carnevale

3.1 Introduction

(1)

3.2 Conservation. Laws and Cascades

(1)

3.3 Markovian Closure

(2)

3.3.1 H-Theorems

(1)

3.4 Numerical Simulations: The Decay Problem

(1)

3.5 A New Scaling Theory for Turbulent Decay

(1)

3.6 A New Dynamic Model for Turbulent Decay

(2)

3.7 Forced Two-Dimensional Turbulence

(1)

3.8 A Question of End States

(3)

3.8.1 Selective Decay

(1)

3.8.2 Arnold Stable States

(1)

3.8.3 Canonical Equilibrium

(1)

3.8.4 Statistics of Point Vortices and Patches

(1)

3.9 Flow over Topography

(2)

3.9.1 Subgrid-Scale Modeling

(2)

3.10 Effects of β

(3)

3.11 Concluding Remarks

(1)

Acknowledgments

(1)

References

(3)

Chapter 4 Statistical Plasma Physics in a Strong Magnetic Field: Paradigms and Problems

(22)

J.A. Krommes

4.1 Introduction

(1)

4.2 Introductory Plasma-Physics Background, Particularly Gyrokinetics

(4)

4.3 Plasma Applications of Statistical Methods

(2)

4.3.1 Gyrokinetic Noise

(1)

4.3.2 Realizable Statistical Closures

(1)

4.4 Statistical Description of Long-Wavelength Flows

(11)

4.4.1 Asymptotic Long-Wavelength Expansion of the EDQNM Formula for Coherent Damping

(2)

4.4.2 Weakly Inhomogeneous Spectral Kinetics and Convective-Cell Growth Rate

(4)

4.4.2.1 General Remarks about Weakly Inhomogeneous Statistics

(1)

4.4.2.2 Modulated Reynolds Stress, Energy Principles, and Use of the Martin—Siggia—Rose Formalism

(3)

4.4.3 Hamiltonian Formalism

(43)

4.4.3.1 Hamiltonian Description of Eulerian Partial Differential Equations

(2)

4.4.3.2 Hamiltonian Description of γq

(1)

4.4.3.3 The Tensor Triad Interaction Time

(1)

4.5 Discussion

(1)

Acknowledgments

(1)

References

(4)

Chapter 5 Some Remarks on Decaying Two-Dimensional Turbulence

(10)

David C. Montgomery

5.1 Introduction

(1)

5.2 The Statistical Mechanics of Vorticity

(3)

5.3 Numerical Results: Rectangular Periodic Boundaries

(1)

5.4 Numerical Results: Material Boundaries

(1)

5.5 Pressure Determinations and Their Ambiguities

(1)

5.6 Summary

(1)

Acknowledgment

(1)

References

(2)

Chapter 6 Statistical and Dynamical Questions in Stratified Turbulence

101

(14)

J.R. Herring, Y. Kimura, R. James, J. Clyne, and P.A. Davidson

6.1 Isotropic Turbulence and Resolution Issues at Large Scales

101

(3)

6.2 Stably Stratified Turbulence

104

(7)

6.3 Concluding Comments

111

(2)

References

113

(2)

Chapter 7 Wavelet Scaling and Navier–Stokes Regularity

115

(10)

Jacques Lewalle

7.1 Background

115

(2)

7.2 Navier—Stokes in Wavelet Space

117

(1)

7.3 Isolated Singularities and Scaling of Wavelet Coefficients

118

(1)

7.4 Evolution of Singularities

119

(1)

7.5 Discussion

120

(2)

References

122

(3)

Chapter 8 Generalization of the Eddy Viscosity Model — Application to a Temperature Spectrum

125

(6)

F. Bataille, G. Brillant, and M. Yousuff Hussaini

8.1 Introduction

125

(1)

8.2 Eddy Viscosity Model

126

(2)

8.2.1 Case 1

126

(1)

8.2.2 Case 2

127

(1)

8.2.3 Case 3

127

(1)

8.2.3.1 Case 3.1

128

(1)

8.2.3.2 Case 3.2

128

(1)

8.3 Application to a Temperature Spectrum

128

(2)

8.3.1 Determination of the Eddy Diffusivity

128

(1)

8.3.2 Determination of the Eddy Diffusivity for the Smagorinsky Model

129

(1)

8.4 Conclusions

130

(1)

References

130

(1)

Chapter 9 Continuous Models for the Simulation of Turbulent Flows: An Overview and Analysis

131

(14)

M. Yousuff Hussaini, Siva Thangam, and Stephen L. Woodruff

9.1 Introduction

131

(3)

9.2 Development of Continuous RANS-LES Models — Possible Bases

134

(2)

9.3 DNS of Kolmogorov Flow

136

(3)

9.4 Continuous RANS-LES Model Development and Application

139

(2)

9.5 Summary and Conclusions

141

(1)

Acknowledgments

141

(1)

References

142

(3)

Chapter 10 Analytical Uses of Wavelets for Navier–Stokes Turbulence

145

(10)

Jacques Lewalle

10.1 Background

145

(2)

10.2 Eliminating Pressure

147

(1)

10.3 Filtered Flexion and Wavelet Transforms

148

(2)

10.4 Applications

150

(2)

10.4.1 Emergence of Structures and Complex Systems Dynamics

150

(1)

10.4.2 Regularity of Euler and NS Solutions

151

(1)

10.4.3 Rapid Distortion Theory

152

(1)

10.4.4 Renormalization Approaches

152

(1)

10.4.5 Structure Functions

152

(1)

10.5 Conclusion

152

(1)

References

153

(2)

Chapter 11 Time Averaging, Hierarchy of the Governing Equations, and the Balance of Turbulent Kinetic Energy

155

(10)

Douglas P. Dokken and Mikhail M. Shvartsman

11.1 Introduction

155

(1)

11.2 Various Notions of Time Averaging

156

(1)

11.2.1 Standard (Reynolds) Time Averaging

156

(1)

11.2.2 Running Time Averaging

157

(1)

11.3 Governing Equations

157

(2)

11.4 Constitutive and Closure Theories

159

(1)

11.5 Turbulent Kinetic Energy

159

(5)

Acknowledgments

164

(1)

References

164

(1)

Chapter 12 The Role of Angular Momentum Invariants in Homogeneous Turbulence

165

(18)

P.A. Davidson

12.1 Introduction

165

(1)

12.2 Loitsyansky's Integral for Isotropic Turbulence

166

(1)

12.3 Kolmogorov's Decay Laws in Isotropic Turbulence

167

(1)

12.4 Landau's Angular Momentum in Isotropic Turbulence

168

(2)

12.5 Long-Range Correlations in Homogenous Turbulence

170

(5)

12.5.1 The Objections of Birkhoff, Batchelor, and Saffman

170

(1)

12.5.2 A Reappraisal of the Long-Range Pressure Forces in E similar to k4 Turbulence

171

(4)

12.6 The Growth of Anisotropy in MHD Turbulence

175

(2)

12.7 The Landau Invariant for Homogeneous MHD Turbulence

177

(1)

12.8 Decay Laws at Low Magnetic Reynolds Number

178

(2)

12.9 A Loitsyansky-type Invariant for Stratified Turbulence

180

(1)

12.10 Conclusions

181

(1)

References

181

(2)

Chapter 13 On the New Concept of Turbulence Modeling in Fully Developed Turbulent Channel Flow and Boundary Layer

183

Ekachai Juntasaro and Varangrat Juntasaro

13.1 Introduction

183

(1)

13.2 Eddy Viscosity Turbulence Modeling

184

(1)

13.3 New Concept of Turbulence Modeling

185

(1)

13.4 Results and Discussion

185

(7)

13.4.1 Fully Developed Turbulent Channel Flow

185

(2)

13.4.2 Turbulent Boundary Layer with Constant Pressure

187

(5)

13.5 Conclusions

192

(1)

Acknowledgments

193

(1)

References

193

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Mathematical and Physical Theory of Turbulence, Volume 250

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