The Navier–Stokes equations, first formulated in 1822, still remain unsolved in the
turbulent regime. Over time, scientists and engineers have been studying
turbulence in more complex systems, such as thermal convection, scalar flows,
flows in magnetofluids, boundary layers, flow across bluff bodies, etc. Turbulent
flows have many complex issues—boundary layers, inhomogeneity and anisotropy,
multiscale complex structures, spatiotemporal correlations among various fields,
etc. In this book we address several fundamental issues of turbulence such as
energy transfers in hydrodynamic, magnetohydrodynamic, scalar, compressible,
anisotropic, and other forms of turbulence; variable energy flux; effects of
enstrophy and kinetic helicity on turbulence.
Author(s): Mahendra K. Verma
Publisher: Cambridge University Press
Year: 2019
Language: English
Pages: 565
Cover......Page 1
Front MAtter
......Page 3
Energy Transfers in Fluid Flows:
Multiscale and Spectral Perspectives......Page 5
Copyright
......Page 6
Dedication
......Page 7
Contents
......Page 9
Preface......Page 21
Acknowledgments
......Page 25
Part I: FORMALISM OF ENERGY TRANSFERS
......Page 29
1 Introduction......Page 31
2 Basics of Hydrodynamics......Page 37
3 Fourier Space Description of
Hydrodynamics......Page 51
4 Energy Transfers in
Hydrodynamic Flows......Page 71
5 Energy Spectrum and Flux of
3D Hydrodynamics......Page 107
6 Enstrophy Transfers in
Hydrodynamics......Page 129
7 Two-dimensional Turbulence......Page 145
8 Helical Turbulence......Page 154
9 Craya{Herring and Helical
Basis......Page 164
10 Field-theoretic Treatment of
Energy Transfers......Page 200
11 Energy Transfers in Anisotropic
Flows......Page 215
12 Turbulence Properties in Real
Space and K41 Theory......Page 224
Part II: FLOWS WITH SCALARS
......Page 241
13 Energy Transfers in Flows with
Scalars......Page 243
14 Flows with a Passive Scalar......Page 257
15 Stably Strati ed Turbulence......Page 273
16 Thermal Convection......Page 290
17 A More Complex Example of an
Active Scalar: Binary Fluid
Mixture......Page 318
Part III: FLOWS WITH VECTORS
......Page 321
18 Energy Transfers in Flows with
Vectors......Page 323
19 Flow with a Passive Vector......Page 333
20 Magnetohydrodynamics:
Formalism......Page 336
21 Energy Transfers in MHD......Page 357
22 Models of MHD Turbulence......Page 386
23 Dynamo: Magnetic Field
Generation in MHD......Page 414
24 Phenomenology of Quasi-static
MHD Turbulence......Page 438
25 Electron
Magnetohydrodynamics......Page 448
Part IV: MISCELLANEOUS FLOWS
......Page 455
26 Rotating Turbulence......Page 457
27 Flow with a Tensor......Page 471
28 Shell Models of Turbulence......Page 480
29 Burgers Turbulence......Page 489
30 Compressible Turbulence......Page 495
31 Miscellaneous Applications of
Energy Transfers......Page 509
32 Conclusions......Page 517
Appendix A.
Power Law Physics......Page 519
Appendix B.
Wealth Distribution and
Cascade in an Economy......Page 521
Appendix C.
Renormalization Group
Analysis of Hydrodynamic
Turbulence......Page 525
Notation......Page 531
References......Page 536
Index......Page 555
