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El. knyga: Turbulence, Coherent Structures, Dynamical Systems and Symmetry

4.33/5 (3 ratings by Goodreads)
(Cornell University, New York), , (Princeton University, New Jersey), (Princeton University, New Jersey)
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"This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures - recurrent patterns - in turbulent flows, it describes mathematical methods that reduce the governing (Navier-Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995"--

"Turbulence pervades our world, from weather patterns to the air entering our lungs. This book describes methods that reveal its structures and dynamics. Building on the existence of coherent structures - recurrent patterns - in turbulent flows, it describes mathematical methods that reduce the governing (Navier-Stokes) equations to simpler forms that can be understood more easily. This second edition contains a new chapter on the balanced proper orthogonal decomposition: a method derived from control theory that is especially useful for flows equipped with sensors and actuators. It also reviews relevant work carried out since 1995. The book is ideal for engineering, physical science and mathematics researchers working in fluid dynamics and other areas in which coherent patterns emerge"--

Recenzijos

'The book commands an impressive bibliography of 396 references, making it an invaluable reference for any researcher who wishes to get into this area of research. The authors have done the best job possible to present this work as carefully and clearly as possible. I strongly recommend the book to everyone who wishes to master this research area, as well as everyone who wants to learn more about the proper orthogonal decomposition method. The research program detailed by the authors is a very promising approach to the problem of the coherent structures of turbulence. Active turbulence researchers, especially researchers who are mainly focused in the engineering applications of turbulence, will find this book a welcome addition to their library.' Eleftherios Gkioulekas, SIAM News

Daugiau informacijos

Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.
Preface to the first edition ix
Preface to the second edition xiii
Acknowledgements xv
PART ONE TURBULENCE
1(152)
1 Introduction
3(14)
1.1 Turbulence
3(2)
1.2 Low-dimensional models
5(3)
1.3 The contents of this book
8(3)
1.4 Notation and mathematical jargon
11(6)
2 Coherent structures
17(51)
2.1 Introduction
17(4)
2.2 Flows with coherent structures
21(11)
2.3 Detection of coherent structures
32(3)
2.4 The mixing layer
35(15)
2.5 The turbulent boundary layer
50(15)
2.6 A preview of things to come
65(3)
3 Proper orthogonal decomposition
68(38)
3.1 Introduction
69(4)
3.2 On domains and averaging
73(1)
3.3 Properties of the POD
74(12)
3.4 Further results
86(5)
3.5 Stochastic estimation
91(2)
3.6 Coherent structures and homogeneity
93(3)
3.7 Some applications
96(4)
3.8 Appendix: some foundations
100(6)
4 Galerkin projection
106(24)
4.1 Introduction
106(4)
4.2 Some simple PDEs revisited
110(6)
4.3 The Navier-Stokes equations
116(5)
4.4 Towards low-dimensional models
121(9)
5 Balanced proper orthogonal decomposition
130(23)
5.1 Balanced truncation
131(2)
5.2 Balanced POD
133(3)
5.3 Output projection
136(1)
5.4 Connections with standard POD
137(2)
5.5 Extensions of balanced POD
139(4)
5.6 Some examples
143(10)
PART TWO DYNAMICAL SYSTEMS
153(100)
6 Qualitative theory
155(35)
6.1 Linearization and invariant manifolds
156(6)
6.2 Periodic orbits and Poincare maps
162(3)
6.3 Structural stability and genericity
165(3)
6.4 Bifurcations local and global
168(11)
6.5 Attractors simple and strange
179(11)
7 Symmetry
190(24)
7.1 Equivariant vector fields
190(4)
7.2 Local bifurcation with symmetry
194(1)
7.3 Global behavior with symmetry
195(7)
7.4 An O (2)-equivariant ODE
202(9)
7.5 Traveling modes
211(3)
8 One-dimensional "turbulence"
214(22)
8.1 Projection onto Fourier modes
215(2)
8.2 Local bifurcations from u = 0
217(3)
8.3 The second bifurcation point
220(6)
8.4 Spatio-temporal chaos
226(10)
9 Randomly perturbed systems
236(17)
9.1 An Ornstein-Uhlenbeck process
237(3)
9.2 Noisy heteroclinic cycles
240(7)
9.3 Power spectra of homoclinic attractors
247(2)
9.4 Symmetry breaking
249(4)
PART THREE THE BOUNDARY LAYER
253(62)
10 Low-dimensional models
255(34)
10.1 Equations for coherent structures
256(3)
10.2 The eigenfunction expansion
259(1)
10.3 Symmetries
260(2)
10.4 Galerkin projection
262(7)
10.5 Geometrical structure of the model
269(3)
10.6 Choosing subspaces and domains
272(3)
10.7 The energy budget
275(6)
10.8 Nonlinear feedback
281(4)
10.9 Interaction with unresolved modes
285(4)
11 Behavior of the models
289(26)
11.1 Backbones for the models
290(3)
11.2 Heteroclinic cycles
293(4)
11.3 Bursts and sweeps
297(2)
11.4 The pressure term
299(4)
11.5 More modes and instabilities
303(4)
11.6 A tentative summary
307(5)
11.7 Appendix: coefficients
312(3)
PART FOUR OTHER APPLICATIONS AND RELATED WORK
315(49)
12 Some other fluid problems
317(28)
12.1 The circular jet
317(4)
12.2 The transitional boundary layer
321(5)
12.3 A forced transitional mixing layer
326(2)
12.4 Flows in complex geometries
328(3)
12.5 "Full channel" wall layer models
331(4)
12.6 Flows in internal combustion engines
335(6)
12.7 A miscellany of results: 1995-2011
341(1)
12.8 Discussion
342(3)
13 Review: prospects for rigor
345(19)
13.1 The quality of models
345(4)
13.2 A short-time tracking estimate
349(3)
13.3 Stability, simulations, and statistics
352(4)
13.4 Spatial localization
356(4)
13.5 The utility of models
360(4)
References 364(18)
Index 382
Philip Holmes is Eugene Higgins Professor of Mechanical and Aerospace Engineering and Professor of Applied and Computational Mathematics, Princeton University. He works on nonlinear dynamics and differential equations. John L. Lumley is Professor Emeritus in the Department of Mechanical and Aerospace Engineering, Cornell University. He has authored or co-authored over two hundred scientific papers and several books. Gahl Berkooz leads the area of Information Management for Ford Motor Company, covering all aspects of Business Information Standards and Integration. Clarence W. Rowley is an Associate Professor of Mechanical and Aerospace Engineering at Princeton University. His research interests lie at the intersection of dynamical systems, control theory and fluid mechanics.
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