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E-raamat: Energy Transfers in Fluid Flows: Multiscale and Spectral Perspectives

(Indian Institute of Technology, Kanpur)
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  • Ilmumisaeg: 23-May-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108226103
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Energy Transfers in Fluid Flows: Multiscale and Spectral PerspectivesSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 23-May-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108226103
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An up-to-date comprehensive text useful for graduate students and academic researchers in the field of energy transfers in fluid flows. The initial part of the text covers discussion on energy transfer formalism in hydrodynamics and the latter part covers applications including passive scalar, buoyancy driven flows, magnetohydrodynamic (MHD), dynamo, rotating flows and compressible flows. Energy transfers among large-scale modes play a critical role in nonlinear instabilities and pattern formation and is discussed comprehensively in the chapter on buoyancy-driven flows. It derives formulae to compute Kolmogorov's energy flux, shell-to-shell energy transfers and locality. The book discusses the concept of energy transfer formalism which helps in calculating anisotropic turbulence.

This is a useful text for graduate students and academic researchers in the field of energy transfers in fluid flows, covering necessary topics such as energy transfers in hydrodynamics, and helical, two-dimensional and three-dimensional hydrodynamic turbulence.

Arvustused

'This book is an outcome of the author's life-long obsession with the mechanism of energy transfers in turbulent flows.' Jayant Bhattacharjee, Indian Association for the Cultivation of Science 'Nicely organized in parts devoted to increasingly complex flows, it is a perfect book to explore the theoretical description of Navier-Stokes turbulence as well as flows with scalars, vectors and more exotic systems.' Daniele Carati, Université Libre de Bruxelles 'This comprehensive book discusses an impressive array of applications from a unified point of view.' Arnab Rai Choudhuri, Indian Institute of Science 'The monograph will be an invaluable resource to students and researchers interested in the application of energy transfer theory to fluids and magnetofluids.' Melvyn Goldstein, NASA 'This book is an outstanding achievement whose many examples and illustrations make the reading as fluid as the subject matter.' Franck Plunian, Université Grenoble Alpes 'It is a self-contained monograph which will certainly be of direct use to a large audience, from graduate students to scholars and researchers.' Annick Pouquet, University of Colorado, Boulder 'This book, addressed to graduate students and researchers, covers vast areas of fluid dynamics and presents each domain in a precise manner.' Maurice Rossi, Université Pierre et Marie Curie, Paris 'This monograph clearly articulates the multiscale energy transfer perspectives for turbulent flows, advanced prominently by the author and his co-workers.' K. R. Sreenivasan, New York University 'This impressive monograph will serve as a highly valuable reference to researchers in turbulence and other fields for many years to come.' P. K. Yeung, Georgia Institute of Technology

Muu info

Provides detailed discussion of topics with applications in the field of energy transfers in fluid flows.
Preface xix
Acknowledgments xxiii
Part I Formalism Of Energy Transfers
1 Introduction
3(6)
1.1 A Generic Nonlinear Equation
4(2)
1.2 Outline of the Book
6(3)
2 Basics of Hydrodynamics
9(14)
2.1 Governing Equations of Incompressible Flows
9(2)
2.2 Vorticity and its Equation
11(1)
2.3 Quadratic Quantities in Hydrodynamics
12(4)
2.4 Conservation Laws in Hydrodynamics
16(6)
Further Reading
22(1)
Exercises
22(1)
3 Fourier Space Description of Hydrodynamics
23(20)
3.1 Fourier Transform and its Properties
23(4)
3.2 Flow Equations in Fourier Space
27(2)
3.3 Vorticity, Kinetic Helicity, and Enstrophy
29(12)
Further Reading
41(1)
Exercises
41(2)
4 Energy Transfers in Hydrodynamic Flows
43(36)
4.1 Mode-to-mode Energy Transfers in Hydrodynamics
44(8)
4.1.1 A physical argument
48(2)
4.1.2 A mathematical argument based on tensor analysis
50(2)
4.2 Energy Transfers in the Presence of Many Triads
52(3)
4.3 Energy Transfers and Equations of Motion for a Two-dimensional Flow
55(4)
4.4 Spectral Energy Flux
59(4)
4.5 Variable Energy Flux
63(4)
4.6 Equivalence between Various Formulas of Energy Flux
67(1)
4.7 Shell-to-shell Energy Transfers
68(3)
4.8 Turbulent Energy Flux and Arrow of Time
71(1)
4.9 Spectral Decomposition, Energy Transfers, and Amplitude Equations
72(1)
4.10 Numerical Simulations Using Spectral Method
73(2)
4.11 Computation of Energy Transfers Using Data
75(2)
Further Reading
77(1)
Exercises
78(1)
5 Energy Spectrum and Flux of 3D Hydrodynamics
79(22)
5.1 Kolmogorov's Theory for 3D Hydrodynamic Turbulence in Spectral Space
79(4)
5.2 Insights from Kolmogorov's Theory of Turbulence
83(3)
5.3 Numerical Verification of Kolmogorov's Theory
86(3)
5.4 Limitations of Kolmogorov's Theory of Turbulence
89(2)
5.5 Energy Spectrum of Turbulent Flow in the Dissipative Regime
91(4)
5.5.1 Pao's model for the inertial-dissipation range of turbulence
92(1)
5.5.2 Pope's model for the inertial-dissipation range of turbulence
93(2)
5.6 Energy Spectrum and Flux for Laminar Flows
95(3)
5.7 Heisenberg's Theory of Turbulence
98(2)
Further Reading
100(1)
Exercises
100(1)
6 Enstrophy Transfers in Hydrodynamics
101(16)
6.1 Mode-to-mode Enstrophy Transfers in Hydrodynamics
101(7)
6.1.1 Derivation of mode-to-mode enstrophy transfer Sωω(k'|p|q)
102(3)
6.1.2 Derivation of mode-to-mode enstrophy transfer Sωu(k'|p|q)
105(3)
6.2 Mode-to-mode Enstrophy Transfers in 2D Hydrodynamics
108(2)
6.3 Enstrophy Transfers for Many Triads
110(1)
6.4 Enstrophy Fluxes
111(3)
6.5 Shell-to-shell Enstrophy Transfer
114(1)
6.6 Numerical Results on Enstrophy Fluxes
114(1)
Further Reading
115(1)
Exercises
116(1)
7 Two-dimensional Turbulence
117(9)
7.1 Conservation Laws; Energy and Enstrophy Transfers in 2D Hydrodynamics
117(2)
7.2 Kraichnan's Theory for 2D Hydrodynamic Turbulence
119(1)
7.3 Subtleties in Energy and Enstrophy Fluxes
119(2)
7.4 Verification of 2D Hydrodynamic Turbulence Models Using Numerical Simulations
121(4)
Further Reading
125(1)
Exercises
125(1)
8 Helical Turbulence
126(10)
8.1 Mode-to-mode Kinetic Helicity Transfers in Hydrodynamics
126(3)
8.2 Flux and Shell-to-shell Transfers of Kinetic Helicity
129(1)
8.3 Phenomenology of Helical Turbulence
130(2)
8.4 Numerical Verification of Kinetic Helicity Spectrum and Flux
132(3)
Further Reading
135(1)
9 Craya-Herring and Helical Basis
136(36)
9.1 Craya-Herring Basis for Hydrodynamics
136(5)
9.2 Equations of Motion in Craya-Herring Basis
141(3)
9.3 Energy Transfer Functions in Craya-Herring Basis
144(3)
9.4 Fluxes in Craya-Herring Basis
147(10)
9.5 Helical Decomposition
157(1)
9.6 Helical Modes
158(5)
9.6.1 The helical mode u+
158(2)
9.6.2 The helical mode u_
160(1)
9.6.3 Mixture of u+ and u_
161(2)
9.7 Equations of Motion in Helical Basis
163(2)
9.8 Mode-to-mode Transfer Functions in Helical Basis
165(2)
9.9 Fluxes and Shell-to-shell Energy Transfers in Helical Basis
167(3)
Further Reading
170(1)
Exercises
170(2)
10 Field-theoretic Treatment of Energy Transfers
172(15)
10.1 Correlation Functions in Homogeneous and Isotropic Turbulence
172(3)
10.2 Field-theoretic Treatment of Mode-to-mode Kinetic Energy Transfers and Flux
175(6)
10.2.1 Computation of (u1(q,t)u1(p,t)u1(k',t)
175(1)
10.2.2 Computation of (u1(q,t)u1(p,t)u2(k',t)
176(3)
10.2.3 Computation of kinetic energy flux and shell-to-shell kinetic energy transfer
179(1)
10.2.4 Energy transfers for absolute equilibrium turbulence or Euler turbulence
180(1)
10.3 Energy and Enstrophy Transfers in 2D Hydrodynamic Turbulence
181(3)
10.4 Kinetic Energy and Helicity Transfers in Helical Turbulence
184(1)
Further Reading
185(1)
Exercises
186(1)
11 Energy Transfers in Anisotropic Flows
187(9)
11.1 Ring Spectrum for Spherical Rings
187(2)
11.2 Ring Spectrum for Cylindrical Rings
189(2)
11.3 Ring-to-ring Energy Transfers
191(1)
11.4 Anisotropic Energy Fluxes, and u left right arrow u uptack Energy Exchange
192(3)
Further Reading
195(1)
12 Turbulence Properties in Real Space and K41 Theory
196(19)
12.1 Second Order Correlation Functions
197(4)
12.2 Third Order Correlation and Structure Functions
201(2)
12.3 Kolmogorov's Theory of Turbulence: Four-fifth Law
203(3)
12.4 Another Derivation of Four-fifth Law-Frisch (1995)
206(1)
12.5 Comparison with Spectral Theory
207(2)
12.6 Higher Order Structure Functions of Hydrodynamic Turbulence
209(3)
Further Reading
212(3)
Part II Flows With Scalars
13 Energy Transfers in Flows with Scalars
215(14)
13.1 Governing Equations
215(3)
13.2 Mode-to-mode Scalar Energy Transfers
218(4)
13.2.1 A physical argument
220(1)
13.2.2 A mathematical argument
220(2)
13.3 Flux and Shell-to-shell Transfers for Scalar Turbulence
222(1)
13.4 Variable Scalar Energy Flux
223(2)
13.5 Scalar Field in Craya-Herring Basis
225(4)
14 Flows with a Passive Scalar
229(16)
14.1 Governing Equations
229(1)
14.2 Phenomenology of Passive Scalar Turbulence
230(1)
14.3 Various Regimes of a Passive Scalar Flow
231(6)
14.3.1 Turbulent regime I: Re 1; Pe 1; Sc < or = to 1
232(1)
14.3.2 Laminar regime: Re < almost = to 1; Pe < almost = to 1
233(1)
14.3.3 Mixed regime I: Re 1; Pe < almost = to 1
234(1)
14.3.4 Mixed regime II: Re < almost = to 1; Pe >1
235(1)
14.3.5 Turbulent regime- II: Re 1; Pe 1; Sc 1
235(2)
14.4 Numerical Simulations of Passive Scalar Turbulence
237(2)
14.4.1 Sc almost = to 1
237(1)
14.4.2 Sc 1
238(1)
14.4.3 Sc 1
238(1)
14.5 Third Order Structure Function for Passive Scalar Turbulence: Four-third Law
239(4)
14.6 Field-theoretic Treatment of Passive Scalar Turbulence
243(1)
Further Reading
243(1)
Exercises
244(1)
15 Stably Stratified Turbulence
245(17)
15.1 Governing Equations in Real Space
245(4)
15.2 Governing Equations in Fourier Space
249(2)
15.3 Energy Transfers and Fluxes for Stably Stratified Turbulence
251(1)
15.4 Various Regimes of Stably Stratified Turbulence
252(1)
15.5 Stably Stratified Turbulence with Moderate Buoyancy
253(8)
15.5.1 Bolgiano-Obukhov phenomenology
253(3)
15.5.2 Modified Bolgiano-Obukhov scaling
256(3)
15.5.3 Numerical results on moderately stratified turbulence
259(2)
15.6 Stably Stratified Turbulence with Strong Buoyancy
261(1)
Further Reading
261(1)
16 Thermal Convection
262(28)
16.1 Governing Equations
262(3)
16.2 Governing Equations in Fourier Space, Energy Transfers, and Fluxes
265(3)
16.3 Structure of Temperature Field in Thermal Convection
268(1)
16.4 Phenomenology of Turbulent Thermal Convection
269(4)
16.5 Structure Functions of Turbulent Thermal Convection
273(2)
16.6 Numerical Verification of the Phenomenology of Turbulent Thermal Convection
275(5)
16.6.1 Kinetic energy spectrum and flux; Scalar energy flux
276(1)
16.6.2 Scalar energy or temperature spectrum
277(1)
16.6.3 Structure functions
278(1)
16.6.4 Shell-to-shell energy transfers
279(1)
16.7 Forcing, Energy Dissipation, and Drag Reduction in Turbulent Convection
280(1)
16.8 Anisotropy in Turbulent Thermal Convection
281(2)
16.9 Various Regimes of Thermal Convection
283(4)
16.9.1 Re 1; Pe 1; Pr almost = to 1
283(1)
16.9.2 Re 1; Pr = 0
284(1)
16.9.3 Re 1; Small Pr
284(2)
16.9.4 Pe 1; Pr = infinity
286(1)
16.10 Two-dimensional Turbulent Thermal Convection
287(1)
Further Reading
288(2)
17 A More Complex Example of an Active Scalar: Binary Fluid Mixture
290(5)
17.1 Dynamics of a Binary Fluid Mixture
290(5)
Part III Flows With Vectors
18 Energy Transfers in Flows with Vectors
295(10)
18.1 Governing Equations
295(3)
18.2 Mode-to-mode Vector Energy Transfers and Energy Fluxes
298(2)
18.3 Variable Vector Energy Flux
300(1)
18.4 Vector Flow in Craya-Herring Basis
301(1)
18.5 Energy Transfers in Craya-Herring and Helical Basis
301(4)
19 Flow with a Passive Vector
305(3)
19.1 Governing Equations
305(1)
19.2 Phenomenology of a Passive Vector Turbulence
306(1)
19.3 Various Regimes of a Passive Vector Flow
307(1)
20 Magnetohydrodynamics: Formalism
308(21)
20.1 Governing Equations in Real Space
308(4)
20.2 Conservation Laws
312(4)
20.3 Governing Equations in Fourier Space
316(4)
20.4 Alfven Waves
320(1)
20.5 MHD Equations in Craya-Herring Basis
321(4)
20.6 MHD Equations in Helical Basis
325(2)
20.7 Nondimensionalized MHD Equations
327(1)
Further Reading
328(1)
Exercises
328(1)
21 Energy Transfers in MHD
329(29)
21.1 Combined Energy Transfers in MHD
329(2)
21.2 Mode-to-mode Energy Transfers in MHD
331(5)
21.3 Mode-to-mode Transfers for Elsaser Variables
336(2)
21.4 Miscellaneous Transfers in MHD
338(4)
21.4.1 Mode-to-mode magnetic helicity transfers in MHD
338(2)
21.4.2 Mode-to-mode kinetic helicity transfers in MHD
340(1)
21.4.3 Mode-to-mode transfers of EA in 2D
341(1)
21.5 Transfers for Many Triads and Fluxes
342(5)
21.6 Variable Energy Fluxes and Conserved Fluxes of MHD Turbulence
347(4)
21.6.1 Kinetic and magnetic energy fluxes
348(2)
21.6.2 Fluxes for Elsaser fields and magnetic helicity
350(1)
21.7 Shell-to-shell Transfers in MHD
351(2)
21.8 Energy Transfers in Craya-Herring Basis
353(1)
21.9 Energy Transfers in Helical Basis
354(2)
Further Reading
356(1)
Exercises
357(1)
22 Models of MHD Turbulence
358(28)
22.1 Models of MHD Turbulence
358(7)
22.1.1 Kraichnan and Iroshnikov's model-E(k) proportional to k-3/2
358(1)
22.1.2 Dobrowonly et al.'s model
359(2)
22.1.3 Model based on energy fluxes
361(1)
22.1.4 Goldreich and Sridhar-E(kuptack) ~ k-5/3uptack
362(1)
22.1.5 Verma-Effective mean magnetic field and E(k) proportional to k-5/3
363(1)
22.1.6 Galtier et al.-Weak turbulence and E(kuptack) proporational to k-2
364(1)
22.1.7 Boldyrev et al.-Dynamic alignment yields k-3/2 spectrum
364(1)
22.2 Third Order Structure Function: Four-third Law
365(5)
22.3 Higher Order Structure Functions of MHD Turbulence
370(1)
22.4 Scaling of cross Helicity and Magnetic Helicity
370(3)
22.4.1 Scaling of cross helicity
371(1)
22.4.2 Scaling of magnetic helicity
372(1)
22.5 MHD Turbulence for Small and Large Prandtl Numbers
373(4)
22.5.1 Energy spectra of small Pm MHD
374(2)
22.5.2 Energy spectra of large Pm MHD
376(1)
22.6 Validation Using Solar Wind
377(3)
22.7 Validation Using Numerical Simulations
380(3)
22.8 MHD Turbulence in the Presence of a Mean Magnetic Field
383(2)
Further Reading
385(1)
23 Dynamo: Magnetic Field Generation in MHD
386(24)
23.1 Definitions
387(1)
23.2 Anti-dynamo Theorems
387(2)
23.3 Energetics of a Dynamo
389(1)
23.4 Kinematic Dynamos
389(8)
23.4.1 Six-mode model-Verma et al. (2008)
389(2)
23.4.2 Roberts dynamo
391(1)
23.4.3 A 2D3C helical dynamo model?
392(1)
23.4.4 A tetrahedron helical dynamo model- Stepanov and Plunian (2018)
393(4)
23.5 Dynamic Dynamos
397(1)
23.5.1 Six-mode model-Verma et al. (2008) revisited
397(1)
23.6 Dynamo Transition and Bifurcation Analysis
397(2)
23.7 Energy Transfers in Turbulent Dynamos
399(8)
23.7.1 Small Pm dynamos
401(2)
23.7.2 Large Pm dynamos
403(2)
23.7.3 Large-scale dynamo with forcing at intermediate scale
405(2)
23.8 Role of Helicities in Dynamos
407(1)
23.9 Analogy between the Vorticity and Magnetic Fields
408(1)
23.10 Turbulent Drag Reduction in MHD
408(1)
Further Reading
409(1)
Exercises
409(1)
24 Phenomenology of Quasi-Static MHD Turbulence
410(10)
24.1 Governing Equations
410(3)
24.2 Distribution and Spectrum of Kinetic Energy
413(5)
24.3 Energy Transfers in Quasi-Static MHD
418(1)
Further Reading
419(1)
25 Electron Magnetohydrodynamics
420(9)
25.1 Governing Equations
420(2)
25.2 Fourier Space Description
422(1)
25.3 Phenomenology of EMHD Turbulence
423(1)
25.3.1 kde 1
423(1)
25.3.2 kde 1
424(1)
25.4 Simplified Version
424(2)
25.4.1 Governing equations and conservation laws
424(1)
25.4.2 Energy transfers in EMHD
425(1)
Further Reading
426(3)
Part IV Miscellaneous Flows
26 Rotating Turbulence
429(14)
26.1 Governing Equations
429(2)
26.2 Properties of Linear Rotating Hydrodynamics
431(2)
26.2.1 Taylor-Proudman theorem
431(1)
26.2.2 Inertial waves in rotating flows
432(1)
26.3 Nonlinear Regime in Rotating Flows
433(1)
26.4 Phenomenology of Rotating Turbulence
434(3)
26.4.1 Zeman's phenomenology
434(1)
26.4.2 Zhou's phenomenology
435(1)
26.4.3 Smith and Waleffe's phenomenology
435(1)
26.4.4 Kuznetsov-Zakharov-Kolmogorov spectrum
436(1)
26.4.5 Inferences from the energy transfers in rotating turbulence
437(1)
26.5 Experimental and Numerical Results on Rotating Turbulence
437(5)
Further Reading
442(1)
27 Flow with a Tensor
443(9)
27.1 Governing Equations
443(2)
27.2 Mode-to-mode Tensor Energy Transfer and Tensor Energy Flux
445(2)
27.3 Energy Spectrum and Flux in a Passive Tensor
447(1)
27.4 Flow with an Active Tensor Field: FENE-p Model
448(2)
27.4.1 Governing equations
448(1)
27.4.2 Energy spectra and fluxes in the FENE-p model
449(1)
27.5 Turbulent Drag Reduction in Polymeric Flows
450(1)
Further Reading
451(1)
28 Shell Models of Turbulence
452(9)
28.1 Shell Model for Hydrodynamic Turbulence
452(6)
28.1.1 Shell model
452(2)
28.1.2 Energy transfers in the shell model
454(4)
28.2 Shell Model for Scalar, Vector, and Tensor Flows
458(2)
Further Reading
460(1)
29 Burgers Turbulence
461(6)
29.1 Governing Equations
461(2)
29.2 Energy Transfers in Burgers Turbulence
463(1)
29.3 Phenomenology of Burgers Turbulence
464(2)
Further Reading
466(1)
30 Compressible Turbulence
467(14)
30.1 Governing Equations
467(3)
30.2 Linear Compressible Flow; Sound Waves
470(1)
30.3 Nearly Incompressible Flow
471(1)
30.4 Fully Compressible Turbulence: Burgers Turbulence Revisited
472(1)
30.5 Equation of Motion of a Compressible Flow in Craya-Herring Basis
473(3)
30.6 Energy Transfers in Compressible Flows
476(4)
30.6.1 Equations for modal kinetic and internal energies
477(1)
30.6.2 Triadic interactions in a compressible flow?
478(1)
30.6.3 Energy fluxes in compressible turbulence
479(1)
Further Reading
480(1)
31 Miscellaneous Applications of Energy Transfers
481(8)
31.1 Variable Enstrophy Flux in 2D Turbulence with Ekman Friction
481(2)
31.2 Energy Transfers in Gyrokinetic Plasma Turbulence
483(1)
31.3 Energy Transfers in Spherical Geometry
484(4)
Further Reading
488(1)
32 Conclusions
489(2)
Appendix A Power Law Physics 491(2)
Further Reading
492(1)
Appendix B Wealth Distribution and Cascade in an Economy 493(4)
Further Reading
496(1)
Appendix C Renormalization Group Analysis of Hydrodynamic Turbulence 497(6)
Further Reading
502(1)
Notation 503(5)
References 508(19)
Subject Index 527(12)
Color Plates 539
Mahendra K. Verma is currently working as Professor in the Department of Physics, Indian Institute of Technology, Kanpur. He has been an associate of the International Centre for Theoretical Physics (ICTP), Italy (200409), and a member of the Program Advisory Committee of Science and Engineering Research Board, India. He works in the broad area of turbulence and nonlinear dynamics, with specialization in magneto hydrodynamics, buoyancy-driven flows, dynamo, and high performance computing. He has been teaching undergraduate and graduate courses at the Indian Institutes of Technology, Kanpur for the past twenty-one years. He has designed and taught courses such as physics of turbulence, magneto hydrodynamics, atmospheric physics, nonlinear physics, computational physics, and introduction to high performance computing for scientists and engineers. He has published more than eighty papers in journals and conferences of national and international repute.
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