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E-raamat: Transport Barriers and Coherent Structures in Flow Data: Advective, Diffusive, Stochastic and Active Methods

(ETH Zurich)
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  • Ilmumisaeg: 16-Mar-2023
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781009225212
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Transport Barriers and Coherent Structures in Flow Data: Advective, Diffusive, Stochastic and Active MethodsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-Mar-2023
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781009225212
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Transport barriers are observed inhibitors of the spread of substances in flows. The collection of such barriers offers a powerful geometric template that frames the main pathways, or lack thereof, in any transport process. This book surveys effective and mathematically grounded methods for defining, locating and leveraging transport barriers in numerical simulations, laboratory experiments, technological processes and nature. It provides a unified treatment of material developed over the past two decades, focusing on the methods that have a solid foundation and broad applicability to data sets beyond simple model flows. The intended audience ranges from advanced undergraduates to researchers in the areas of turbulence, geophysical flows, aerodynamics, chemical engineering, environmental engineering, flow visualization, computational mathematics and dynamical systems. Detailed open-source implementations of the numerical methods are provided in an accompanying collection of Jupyter notebooks linked from the electronic version of the book.

Providing a unified treatment of recent advances, this book surveys effective and mathematically grounded methods for defining, locating and leveraging transport barriers. An excellent resource for advanced undergraduates and above, it includes links to an extensive collection of numerical demonstrations in Jupyter notebooks.

Arvustused

'This is a must read for anyone interested in data-driven fluid mechanics. Coherent structures are central to how we understand fluids, and Haller has been a pioneer in this field for decades. This book covers an exciting range of topics from introductory to advanced material, complete with beautiful graphics and illustrations.' Steven L. Brunton, University of Washington 'George Haller has written a clear, well-illustrated text that step-by-step explains the mathematics needed to understand and quantify fluid motions that cause mixing and describes and identifies the corresponding transport barriers to mixing processes. The ideas are introduced in a systematic way, with examples that highlight analytical features, software available via github, and interpretations to help the reader build intuition for the mathematical concepts and their application to physical processes.' Howard A. Stone, Princeton University 'Dynamical systems theory was developed in the 1980s, but for fluid dynamics has not played the prominent role it deserves. The present insightful and well-written book `Transport Barriers and Coherent Structure in Flow Data' by George Haller now bridges this gap between modern fluid dynamics and dynamical systems theory. It is based on mathematically grounded and solid methods, which are then applied to fluid dynamical problems and data sets. It also includes the usage of modern data-driven methods. The book is complemented by clickable links to a library of numerical implementations of transport barrier detection methods. It is a wonderful textbook for Turbulence and Advanced Fluid Mechanics classes for students in Applied Mathematics, Physics, and Mechanical and Chemical Engineering alike and unmissable for scientists working at the interface between dynamical systems theory and fluid dynamics.' Detlef Lohse, University of Twente ' essential reading in areas related to chemical engineering, geophysical flows, and aerodynamics, to name a few of its applications. Highly recommended.' R. N. Laoulache, Choice

Muu info

Explore a wealth of proven mathematical methods for uncovering transport barriers in numerical, experimental and observational flow data.
Preface xiii
Acknowledgments xvi
1 Introduction
1(12)
1.1 The Mathematics of Transport Barriers
2(1)
1.2 The Physics of Transport Barriers
3(1)
1.3 Idealized Transport Barriers vs. Finite-Time Coherent Structures
4(1)
1.4 Transport Barriers in Flow Separation and Attachment
4(2)
1.5 Transport Barriers in Inertial Particle Motion
6(1)
1.6 Barriers to Diffusive and Stochastic Transport
7(1)
1.7 Barriers to Dynamically Active Transport
8(1)
1.8 Coherent Sets, Coherence Clusters and Coherent States
9(4)
2 Eulerian and Lagrangian Fundamentals
13(47)
2.1 Eulerian Description of Fluid Motion
14(5)
2.1.1 Eulerian Scalars, Vector Fields and Tensors
14(1)
2.1.2 Streamlines and Stagnation Points in 2D Flows
15(2)
2.1.3 Streamsurfaces and Stagnation Points in 3D Flows
17(1)
2.1.4 Irrotational and Inviscid Flows
18(1)
2.2 Lagrangian Description of Fluid Motion
19(29)
2.2.1 Steady Flows as Autonomous Dynamical Systems
20(1)
2.2.2 The Extended Phase Space
21(1)
2.2.3 The Flow Map and Its Gradient
21(2)
2.2.4 Material Surfaces, Material Lines and Streaklines
23(3)
2.2.5 Invariant Manifolds
26(1)
2.2.6 Evolution of Material Volume and Mass
26(2)
2.2.7 Topological Equivalence and Structural Stability
28(1)
2.2.8 Linearized Flow: The Equation of Variations
29(2)
2.2.9 When Are the Eigenvalues of Vv Relevant?
31(1)
2.2.10 Lagrangian Aspects of the Vorticity
32(2)
2.2.11 Dynamics Near Fixed Points of Steady Flows
34(1)
2.2.12 Poincare Maps
34(6)
2.2.13 Revisiting Initial Conditions: Poincare's Recurrence Theorem
40(2)
2.2.14 Convergence of Time-Averaged Observables: Ergodic Theorems
42(2)
2.2.15 Lagrangian Scalars, Vector Fields and Tensors
44(4)
2.3 Lagrangian Decompositions of Infinitesimal Material Deformation
48(8)
2.3.1 Singular Value Decomposition (SVD)
48(2)
2.3.2 Polar Decomposition
50(3)
2.3.3 Dynamic Polar Decomposition (DPD)
53(3)
2.4 Are the Eulerian and Lagrangian Approaches Equivalent?
56(2)
2.5 Summary and Outlook
58(2)
3 Objectivity of Transport Barriers
60(38)
3.1 Common Misinterpretations of the Principle of Material Frame-Indifference
62(1)
3.2 Objectivity Yields the Navier-Stokes Equation in Arbitrary Frames
63(1)
3.3 Eulerian Objectivity
64(8)
3.3.1 Objectivity of Eulerian Scalar Fields
65(1)
3.3.2 Objectivity of Eulerian Vector Fields
66(3)
3.3.3 Objectivity of Eulerian Tensor Fields
69(2)
3.3.4 Galilean Invariance
71(1)
3.4 Lagrangian Objectivity
72(2)
3.4.1 Objectivity of Lagrangian Scalar Fields
72(1)
3.4.2 Objectivity of Lagrangian Vector Fields
73(1)
3.4.3 Objectivity of Lagrangian Tensor Fields
73(1)
3.5 Eulerian--Lagrangian Objectivity of Two-Point Tensors
74(3)
3.5.1 Objectivity of the Decompositions of the Deformation Gradient
75(2)
3.6 Quasi-Objectivity
77(1)
3.7 Some Nonobjective Approaches to Transport Barriers
77(19)
3.7.1 Nonobjective Eulerian Principles
78(8)
3.7.2 Objectivization of Nonobjective Eulerian Coherence Principles
86(4)
3.7.3 Nonobjective Lagrangian Principles
90(6)
3.8 Summary and Outlook
96(2)
4 Barriers to Chaotic Advection
98(43)
4.1 2D Time-Periodic Rows
99(12)
4.1.1 Hyperbolic Barriers to Transport
102(4)
4.1.2 Elliptic Barriers to Transport
106(4)
4.1.3 Parabolic Barriers to Transport
110(1)
4.2 2D Time-Quasiperiodic Flows
111(2)
4.3 2D Recurrent Flows with a First Integral
113(8)
4.3.1 Barriers from First Integrals in Time-Periodic Flows
115(2)
4.3.2 Barriers from First Integrals in Time-Quasiperiodic Flows
117(4)
4.4 3D Steady Flows
121(14)
4.4.1 Definition of Transport Barriers from First-Return Maps
121(1)
4.4.2 Transport Barriers vs. Streamsurfaces and Sectional Streamlines
121(4)
4.4.3 Transport Barriers in 3D Steady Inviscid Flows
125(5)
4.4.4 Transport Barriers in 3D Steady Flows with a Continuous Symmetry
130(3)
4.4.5 Transport Barriers from Ergodic Theory
133(2)
4.5 Barriers in 3D Time-Periodic Flows
135(1)
4.6 Burning Invariant Manifolds: Transport Barriers in Reacting Flows
136(3)
4.7 Summary and Outlook
139(2)
5 Lagrangian and Objective Eulerian Coherent Structures
141(101)
5.1 Tracer-Transport Barriers in Nondiffusive Passive Tracer Fields
144(4)
5.2 Advective Transport Barriers as LCSs
148(28)
5.2.1 Hyperbolic LCS from the Finite-Time Lyapunov Exponent
149(1)
5.2.2 FTLE Ridges Are Necessary (but Not Sufficient) Indicators of Hyperbolic LCS
150(3)
5.2.3 Extraction Interval and Convergence of the FTLE
153(1)
5.2.4 Numerical Computation of the FTLE
154(2)
5.2.5 Extraction of FTLE Ridges
156(1)
5.2.6 Hyperbolic LCSs vs. Stable and Unstable Manifolds in Temporally Recurrent Flows
156(2)
5.2.7 Repelling and Attracting LCSs from the Same Calculation
158(2)
5.2.8 FTLE vs. Finite-Size Lyapunov Exponents (FSLE)
160(1)
5.2.9 Parabolic LCSs from FTLE
161(3)
5.2.10 Elliptic LCSs from the Polar Rotation Angle (PRA)
164(5)
5.2.11 Elliptic LCSs from the Lagrangian-Averaged Vorticity Deviation
169(7)
5.3 Local Variational Theory of LCSs
176(17)
5.3.1 Local Variational Theory of Hyperbolic LCSs
177(9)
5.3.2 Local Variational Theory of Elliptic LCSs
186(6)
5.3.3 Local Variational Theory of Parabolic LCSs
192(1)
5.4 Global Variational Theory of LCSs
193(19)
5.4.1 Elliptic LCSs in 2D: Black-Hole Vortices
194(6)
5.4.2 Computing Elliptic LCSs as Closed Null-Geodesies
200(3)
5.4.3 Shearless LCSs in 2D: Parabolic and Hyperbolic Barriers
203(5)
5.4.4 Unified Variational Theory of Elliptic and Hyperbolic LCSs in 3D
208(4)
5.5 Adiabatically Quasi-Objective, Single-Trajectory Diagnostics for Transport Barriers
212(8)
5.5.1 Adiabatically Quasi-Objective Diagnostic for Material Stretching
213(2)
5.5.2 Adiabatically Quasi-Objective Diagnostic for Material Rotation
215(2)
5.5.3 Single-Trajectory, Adiabatically Quasi-Objective LCS Computations for the AVISO Data Set
217(1)
5.5.4 Adiabatically Quasi-Objective Material Eddy Extraction from Actual Ocean Drifters
218(2)
5.6 Elliptic-Parabolic-Hyperbolic (EPH) Partition and LCSs
220(6)
5.7 Objective Eulerian Coherent Structures (OECSs)
226(14)
5.7.1 Instantaneous Limit of the Flow Map
227(1)
5.7.2 Instantaneous FTLE
228(1)
5.7.3 Instantaneous Vorticity Deviation (IVD)
229(1)
5.7.4 Global Variational Theory of OECS in 2D Flows
230(10)
5.8 Summary and Outlook
240(2)
6 Flow Separation and Attachment Surfaces as Transport Barriers
242(33)
6.1 Flow Separation in Steady and Recurrent Flows
243(16)
6.1.1 Separation in 2D Steady Flows
243(5)
6.1.2 Separation in 2D Time-Periodic Flows
248(3)
6.1.3 Separation in 3D Steady Flows
251(5)
6.1.4 Separation in 3D Recurrent Flows
256(3)
6.2 Unsteady Flow Separation Created by LCSs
259(14)
6.2.1 2D Unsteady Separation
259(12)
6.2.2 3D Fixed Unsteady Separation
271(2)
6.3 Summary and Outlook
273(2)
7 Inertial LCSs: Transport Barriers in Finite-Size Particle Motion
275(25)
7.1 Equation of Motion for Inertial Particles
276(1)
7.2 Relationship between Inertial and Fluid Motion
277(3)
7.3 The Divergence of the Inertial Equation and the Q Parameter
280(1)
7.4 Transport Barriers for Neutrally Buoyant Particles
281(2)
7.5 Transport Barriers for Neutrally Buoyant Particles with Propulsion
283(2)
7.6 Transport Barriers for Aerosols and Bubbles
285(7)
7.6.1 Attracting iLCS in 2D Steady Flows
286(1)
7.6.2 Attracting iLCS in 3D Steady Flows
286(2)
7.6.3 Attracting iLCS in 2D Time-Periodic Flows
288(2)
7.6.4 Attracting iLCS in General 3D Flows
290(2)
7.7 Inertial Transport Barriers in Rotating Frames
292(3)
7.8 Inertial Transport on the Ocean Surface: Modeling and Machine Learning
295(3)
7.9 Summary and Outlook
298(2)
8 Passive Barriers to Diffusive and Stochastic Transport
300(31)
8.1 Unconstrained Diffusion Barriers in Incompressible Flows
302(10)
8.1.1 Unconstrained Diffusion Barriers in 2D Flows
306(6)
8.2 Constrained Diffusion Barriers in Incompressible Flows
312(2)
8.2.1 Constrained Diffusion Extremizers in 2D Flows
313(1)
8.3 Barriers to Diffusive Vorticity Transport in 2D Flows
314(6)
8.3.1 An Analytic Example: Vorticity Transport Barriers in a Decaying Channel Flow
316(2)
8.3.2 Numerical Examples: Vorticity Transport Barriers as Vortex Boundaries in Turbulence
318(2)
8.4 Diffusion Barriers in Compressible Flows
320(3)
8.5 Transport Barriers in Stochastic Velocity Fields
323(5)
8.6 Exploiting Diffusion Barriers for Climate Geoengineering
328(2)
8.7 Summary and Outlook
330(1)
9 Dynamically Active Barriers to Transport
331(36)
9.1 Setup
332(1)
9.2 Active Transport Through Material Surfaces
333(3)
9.3 Lagrangian Active Barriers
336(1)
9.4 Eulerian Active Barriers
337(1)
9.5 Active Barrier Equations for Momentum and Vorticity
338(2)
9.5.1 Barriers to Linear Momentum Transport
338(1)
9.5.2 Barriers to Angular Momentum Transport
339(1)
9.5.3 Barriers to Vorticity Transport
339(1)
9.6 Examples of Active Transport Barriers
340(7)
9.6.1 Active Transport Barriers in General 2D Navier-Stokes Flows
341(4)
9.6.2 Directionally Steady Beltrami Flows
345(2)
9.7 Active LCS Methods for Barrier Detection
347(8)
9.7.1 Active Poincare Maps
349(1)
9.7.2 Active FTLE (aFTLE) and Active TSE (aTSE)
349(3)
9.7.3 Active PRA (aPRA) and Active TRA (aTRA)
352(2)
9.7.4 The Choice of the Maximal Barrier Time, sjv in Active LCS Diagnostics
354(1)
9.7.5 Relationship between Active and Passive LCS Diagnostics
355(1)
9.8 Active Barriers in 2D and 3D Turbulence Simulations
355(11)
9.8.1 2D Homogeneous, Isotropic Turbulence
356(3)
9.8.2 3D Turbulent Channel Flow
359(1)
9.8.3 Eulerian Active Barriers from the Normalized Barrier Equation
359(4)
9.8.4 Turbulent Momentum Transport Barriers (MTBs)
363(1)
9.8.5 Momentum-Trapping Vortices in Turbulent Channel Flows
364(2)
9.9 Summary and Outlook
366(1)
Appendix 367(23)
References 390(16)
Index 406
George Haller holds the Chair in Nonlinear Dynamics at the Institute of Mechanical Systems of ETH Zürich. Previously, he held tenured faculty positions at Brown University, McGill University and MIT. For his research in nonlinear dynamical systems, he has received numerous recognitions including a Sloan Fellowship, an ASME T. Hughes Young Investigator award, a Manning Assistant Professorship at Brown and a Faculty of Engineering Distinguished Professorship at McGill. He is an elected fellow of the SIAM, APS, ASME and an external member of the Hungarian Academy of Science. He is the author of more than 150 publications.
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