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E-grāmata: Mathematical and Physical Theory of Turbulence, Volume 250 [Taylor & Francis e-book]

Edited by (University of Central Florida, Orlando, USA), Edited by (University of Central Florida, Orlando, USA)
  • Formāts: 208 pages, 1 Tables, black and white; 4 Halftones, black and white; 46 Illustrations, black and white
  • Sērija : Lecture Notes in Pure and Applied Mathematics
  • Izdošanas datums: 15-Jun-2006
  • Izdevniecība: Marcel Dekker Inc
  • ISBN-13: 9780429133800
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  • Taylor & Francis e-book
  • Cena: 293,49 €*
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  • Standarta cena: 419,27 €
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Mathematical and Physical Theory of Turbulence, Volume 250Palielināt
  • Formāts: 208 pages, 1 Tables, black and white; 4 Halftones, black and white; 46 Illustrations, black and white
  • Sērija : Lecture Notes in Pure and Applied Mathematics
  • Izdošanas datums: 15-Jun-2006
  • Izdevniecība: Marcel Dekker Inc
  • ISBN-13: 9780429133800
Citas grāmatas par šo tēmu:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Rokasgrāmatas mājas lapa: https://www.taylorfrancis.com/books/9780429133800
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)
1.2 Henry Whitehead
2(1)
1.3 Jean-Pierre Serre
3(1)
1.4 Epilogue
4(3)
Chapter 2 Lagrangian Description of Turbulence 7(40)
Gregory Falkovich
2.1 Introduction
8(2)
2.1.1 Propagators
8(1)
2.1.2 Kraichnan Model
9(1)
2.1.3 Large Deviation Approach
10(1)
2.2 Particles in Fluid Turbulence
10(15)
2.2.1 Single-Particle Diffusion
11(1)
2.2.2 Two-Particle Dispersion in a Spatially Smooth Velocity
12(3)
2.2.3 Two-Particle Dispersion in a Nonsmooth Incompressible Flow
15(3)
2.2.4 Two-Particle Dispersion in a Compressible Flow
18(2)
2.2.5 Multiparticle Configurations and Zero Modes
20(5)
2.3 Unforced Evolution of Passive Fields
25(6)
2.3.1 Decay of Tracer Fluctuations
25(4)
2.3.1.1 Smooth Velocity
26(1)
2.3.1.2 Nonsmooth Velocity
27(1)
2.3.1.3 Scalar Decay with Viscous and Inertial Intervals Present
28(1)
2.3.1.4 Scalar Decay in a Finite Box
28(1)
2.3.2 Growth of Density Fluctuations in Compressible Flow
29(1)
2.3.3 Vector Fields in a Smooth Velocity
30(1)
2.3.3.1 Gradients of the Passive Scalar
30(1)
2.3.3.2 Small-Scale Magnetic Dynamo
31(1)
2.4 Cascades of a Passive Tracer
31(6)
2.4.1 Direct Cascade
32(5)
2.4.1.1 Direct Cascade in a Smooth Velocity
33(1)
2.4.1.2 Anomalies of Tracer Statistics in a Nonsmooth Velocity
34(3)
2.4.2 Inverse Cascade in a Compressible Flow
37(1)
2.5 Active Tracers
37(5)
2.5.1 Activity Changing Cascade Direction
38(3)
2.5.1.1 Burgers Turbulence
38(2)
2.5.1.2 Two-Dimensional Magnetohydrodynamics
40(1)
2.5.2 Two-Dimensional Incompressible Turbulence
41(8)
2.5.2.1 Direct Vorticity Cascade in Two Dimensions
41(1)
2.5.2.2 Inverse Energy Cascade in Two Dimensions
42(1)
2.6 Conclusion
42(1)
Acknowledgment
43(1)
References
43(4)
Chapter 3 Two-Dimensional Turbulence: An Overview 47(22)
George F. Carnevale
3.1 Introduction
47(1)
3.2 Conservation. Laws and Cascades
48(1)
3.3 Markovian Closure
49(2)
3.3.1 H-Theorems
50(1)
3.4 Numerical Simulations: The Decay Problem
51(1)
3.5 A New Scaling Theory for Turbulent Decay
52(1)
3.6 A New Dynamic Model for Turbulent Decay
53(2)
3.7 Forced Two-Dimensional Turbulence
55(1)
3.8 A Question of End States
56(3)
3.8.1 Selective Decay
56(1)
3.8.2 Arnold Stable States
57(1)
3.8.3 Canonical Equilibrium
57(1)
3.8.4 Statistics of Point Vortices and Patches
58(1)
3.9 Flow over Topography
59(2)
3.9.1 Subgrid-Scale Modeling
59(2)
3.10 Effects of β
61(3)
3.11 Concluding Remarks
64(1)
Acknowledgments
65(1)
References
66(3)
Chapter 4 Statistical Plasma Physics in a Strong Magnetic Field: Paradigms and Problems 69(22)
J.A. Krommes
4.1 Introduction
69(1)
4.2 Introductory Plasma-Physics Background, Particularly Gyrokinetics
70(4)
4.3 Plasma Applications of Statistical Methods
74(2)
4.3.1 Gyrokinetic Noise
74(1)
4.3.2 Realizable Statistical Closures
75(1)
4.4 Statistical Description of Long-Wavelength Flows
76(11)
4.4.1 Asymptotic Long-Wavelength Expansion of the EDQNM Formula for Coherent Damping
77(2)
4.4.2 Weakly Inhomogeneous Spectral Kinetics and Convective-Cell Growth Rate
79(4)
4.4.2.1 General Remarks about Weakly Inhomogeneous Statistics
79(1)
4.4.2.2 Modulated Reynolds Stress, Energy Principles, and Use of the Martin—Siggia—Rose Formalism
80(3)
4.4.3 Hamiltonian Formalism
83(43)
4.4.3.1 Hamiltonian Description of Eulerian Partial Differential Equations
83(2)
4.4.3.2 Hamiltonian Description of γq
85(1)
4.4.3.3 The Tensor Triad Interaction Time
86(1)
4.5 Discussion
87(1)
Acknowledgments
87(1)
References
87(4)
Chapter 5 Some Remarks on Decaying Two-Dimensional Turbulence 91(10)
David C. Montgomery
5.1 Introduction
91(1)
5.2 The Statistical Mechanics of Vorticity
92(3)
5.3 Numerical Results: Rectangular Periodic Boundaries
95(1)
5.4 Numerical Results: Material Boundaries
96(1)
5.5 Pressure Determinations and Their Ambiguities
97(1)
5.6 Summary
98(1)
Acknowledgment
98(1)
References
99(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


John Cannon, Bhimsen Shivamoggi
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