Energy Transfers in Fluid Flows: Multiscale and Spectral Perspectives

Description

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. 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 Stratied 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