An Informal Introduction to Turbulence

by Tsinober, Arkady

• ISBN13: 9781402001666
• ISBN10: 1402001665
• Format: Paperback
• Copyright: 2002-01-01
• Publisher: Springer Verlag

Summary

This book is an informal introduction to the turbulence of fluids. The emphasis is placed on turbulence as a physical phenomenon. It addresses the unresolved issues, misconceptions, controversies, and major problems of the turbulence of fluids rather than the conventional formalistic elements and models. Little use is made of complicated formalisms; instead the emphasis is placed on an essentially informal qualitative form. The scope of the book is focused on the purely basic aspects of the turbulent flows of incompressible fluids. This book will certainly be of interest and use to graduate students as well as scientists active in fields where the turbulence of fluids is of importance. The book is intentionally written to appeal to a broad readership with the aim of making the turbulence of fluids interesting and comprehensible to the interested engineer.

Table of Contents

Introduction	1	(27)
Brief history	1	(1)
Nature and major qualitative universal features of turbulent flows	2	(17)
Representative examples of turbulent flows	2	(13)
In lieu of definition: major qualitative universal features of turbulent flows	15	(4)
Why turbulence is so impossibly difficult? The three N's	19	(6)
On the Navier-Stokes equations	19	(2)
On the nature of the problem	21	(1)
Nonlinearity	22	(1)
Noninegrability	22	(1)
Nonlocality	23	(1)
On physics of turbulence	24	(1)
On statistical theories	24	(1)
Outline of the following material	25	(1)
In lieu of summary	26	(1)
Origins of Turbulence	27	(6)
Instability	27	(2)
Transition to turbulence versus routes to chaos	29	(2)
Many ways of creating turbulent flows	31	(1)
Summary	32	(1)
Methods of Describing of Turbulent Flows	33	(14)
Deterministic versus random/stochastic or how `statistical' is turbulence?	34	(3)
On statistical theories, reduced (low dimensional) representations and related matters	37	(3)
Turbulence versus deterministic chaos	40	(1)
Statistical methods of looking at the data only? Or what kind of statistics one needs?	41	(2)
Decompositions/representations	43	(2)
Summary	45	(2)
Kinematics	47	(18)
Passive objects in random fluid flows	47	(9)
Geometrical statistics	53	(3)
Kinematic/Lagrangian chaos/advection	56	(3)
On the relation between Eulerian and Lagrangian fields	59	(1)
On analogies and relations between passive and active fields	60	(2)
Summary	62	(3)
Phenomenology	65	(18)
Introductory notes	65	(1)
Kolmogorov phenomenology and related subjects	66	(7)
Cascade	73	(4)
Introduction	73	(1)
Is there cascade in physical space?	74	(3)
What are the `small scales' in turbulent flows?	77	(3)
Cascade of passive objects?	80	(1)
Summary	81	(2)
Dynamics	83	(68)
Introduction	83	(2)
Why velocity derivatives?	85	(7)
Vortex stretching and enstrophy production	86	(3)
Why strain too?	89	(3)
Self-amplification of the field of velocity derivatives	92	(6)
Geometrical statistics	98	(15)
Alignments	100	(1)
The geometry of vortex stretching	101	(12)
Depression of nonlinearity	113	(5)
Relative depression of nonlinearity in regions with concentrated vorticity	114	(1)
Are regions of concentrated vorticity quasionedimensional?	115	(3)
Nonlocality	118	(12)
Introduction and simple examples	118	(3)
Different aspects of nonlocality	121	(9)
Acceleration and related matters	130	(10)
The relation between the total acceleration and its local and convective components	131	(4)
The relation between the total acceleration and its irrotational and solenoidal components	135	(2)
Scale dependence	137	(2)
Kinematical versus dynamical effects	139	(1)
Non-Gaussian nature of turbulence	140	(11)
Odd moments	141	(2)
Quasi-Gaussian manifestations	143	(4)
Irreversibility of turbulence	147	(1)
Summary	148	(3)
Structure(S) of Turbulent Flows	151	(30)
Introduction	151	(1)
Intermittency	152	(13)
What is small scale intermittency?	153	(1)
Measures/manifestations of intermittency	154	(8)
On possible origins of small scale intermittency	162	(3)
What is(are) structure(s) of turbulent flows?	165	(11)
On the origins of structure(s) of/in turbulence	165	(3)
How does the structure of turbulence `look'?	168	(2)
Structure versus statistics	170	(3)
Examples of statistics weakly sensitive to structure(s)	173	(1)
Structure sensitive statistics	174	(2)
Which quantities possess structure in turbulence and how to `dig' them out?	176	(5)
Structure(s) versus scales and decompositions	177	(1)
Summary	178	(3)
Turbulence Under Various Influences and Physical Circumstances	181	(46)
Introduction	181	(2)
Shear flows	183	(9)
Partly turbulent flows - entrainment	192	(4)
Variable density	196	(7)
Convection	196	(3)
Stable stratification	199	(4)
Compressible flows	203	(1)
Rotation	203	(3)
Helicity	206	(1)
Negative eddy viscosity phenomena	206	(5)
Laboratory experiments	207	(3)
Examples from geophysics	210	(1)
Possible explanations	211	(1)
Magnetohydrodynamic flows	211	(3)
Two-dimensional turbulence	214	(6)
Pure two-dimensional versus quasi-two-dimensional	216	(2)
Some additional differences between two-dimensional and three-dimensional turbulence	218	(2)
Additives	220	(7)
Conclusion/Close	227	(10)
Universality	227	(6)
On universal aspects of turbulence structure	228	(2)
Reynolds number dependence	230	(2)
Self-amplification of velocity derivatives	232	(1)
Depression of nonlinearity	233	(1)
Some mathematical and related aspects	233	(2)
On the goals of basic research in turbulence	235	(2)
Appendix A. What is Turbulence?	237	(6)
Appendix B. About the 'Snags' of the Problem	243	(4)
Appendix C. Glossary of Essential Fluid Mechanics	247	(22)
Kinematics	247	(1)
Dynamics	248	(9)
Basic equations and their consequences	248	(6)
Some additional consequences from the NSE and invariant quantities	254	(2)
Symmetries of Euler and Navier-Stokes equations	256	(1)
Passive objects	257	(2)
Passive scalars	257	(1)
Passive vectors	257	(2)
Some basic relations for the statistical description of turbulent flows	259	(10)
Scaling, scales and related matters	260	(3)
Reynolds averaged Navier-Stokes equations and related	263	(3)
Filter decomposition	266	(1)
Equations governing the dynamics of `error'	267	(2)
Appendix D. It is a Misconception That	269	(2)
Appendix E. On Methods of Studing Turbulent Flows	271	(4)
Direct numerical simulations of the Navier-Stokes equations	271	(1)
Physical experiments	272	(3)
Appendix F. Glossary of Some Terms	275	(2)
Bibliography	277	(36)
Author Index	313	(8)
Subject Index	321