Wu / Ma / Zhou Vorticity and Vortex Dynamics

1. Auflage 2007
ISBN: 978-3-540-29028-5
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 776 Seiten

Autoren/Hrsg.

Wu, Jie-Zhi

Ma, Hui-yang

Zhou, M.-D.

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;Introduction;15
3.1;Fundamental Processes in Fluid Dynamics and Their Coupling;16
3.2;Historical Development;17
3.3;The Contents of the Book;20
4;Vorticity Dynamics;24
4.1;Fundamental Processes in Fluid Motion;25
4.1.1;Basic Kinematics;25
4.1.2;Fundamental Equations of Newtonian Fluid Motion;37
4.1.3;Intrinsic Decompositions of Vector Fields;48
4.1.4;Splitting and Coupling of Fundamental Processes;60
4.1.5;Summary;75
4.2;Vorticity Kinematics;78
4.2.1;Physical Interpretation of Vorticity;78
4.2.2;Vorticity Integrals and Far-Field Asymptotics;82
4.2.3;Lamb Vector and Helicity;96
4.2.4;Vortical Impulse and Kinetic Energy;105
4.2.5;Vorticity Evolution;111
4.2.6;Circulation-Preserving Flows;120
4.2.7;Summary;138
4.3;Fundamentals of Vorticity Dynamics;141
4.3.1;Vorticity Diffusion Vector;141
4.3.2;Vorticity Field at Small Reynolds Numbers;160
4.3.3;Vorticity Dynamics in Boundary Layers;171
4.3.4;Vortex Sheet Dynamics;182
4.3.5;Vorticity-Based Formulation of Viscous Flow Problem;195
4.3.6;Summary;209
4.4;Vorticity Dynamics in Flow Separation;211
4.4.1;Flow Separation and Boundary-Layer Separation;211
4.4.2;Three-Dimensional Steady Flow Separation;214
4.4.3;Steady Boundary Layer Separation;226
4.4.4;Unsteady Separation;244
4.4.5;Summary;261
5;Vortex Dynamics;263
5.1;Typical Vortex Solutions;264
5.1.1;Governing Equations;264
5.1.2;Axisymmetric Columnar Vortices;269
5.1.3;Circular Vortex Rings;281
5.1.4;Exact Strained Vortex Solutions;293
5.1.5;Asymptotic Strained Vortex Solutions;304
5.1.6;On the Definition of Vortex;319
5.1.7;Summary;329
5.2;Separated Vortex Flows;331
5.2.1;Topological Theory of Separated Flows;331
5.2.2;Steady Separated Bubble Flows in Euler Limit;347
5.2.3;Steady Free Vortex-Layer Separated Flow;360
5.2.4;Unsteady Bluff-Body Separated Flow;374
5.2.5;Summary;389
5.3;Core Structure, Vortex Filament, and Vortex System;391
5.3.1;Vortex Formation and Core Structure;391
5.3.2;Dynamics of Three-Dimensional Vortex Filament;407
5.3.3;Motion and Interaction of Multiple Vortices;426
5.3.4;Vortex–Boundary Interactions;442
5.3.5;Summary;454
6;Vortical Flow Instability, Transition and Turbulence;456
6.1;Vortical-Flow Stability and Vortex Breakdown;457
6.1.1;Fundamentals of Hydrodynamic Stability;457
6.1.2;Shear-Flow Instability;475
6.1.3;Instability of Axisymmetric Columnar Vortices;486
6.1.4;Instabilities of Strained Vortices;498
6.1.5;Vortex Breakdown;508
6.1.6;Summary;521
6.2;Vortical Structures in Transitional and Turbulent Shear Flows;525
6.2.1;Coherent Structures;526
6.2.2;Vortical Structures in Free Shear Flows;532
6.2.3;Vortical Structures in Wall-Bounded Shear Layers;541
6.2.4;Some Theoretical Aspects in Studying Coherent Structures;556
6.2.5;Two Basic Processes in Turbulence;567
6.2.6;Vortical Structures in Other Shear Flows;579
6.2.7;Summary;589
7;Special Topics;591
7.1;Vortical Aerodynamic Force and Moment;592
7.1.1;Introduction;592
7.1.2;Projection Theory;599
7.1.3;Vorticity Moments and Classic Aerodynamics;604
7.1.4;Boundary Vorticity-Flux Theory;613
7.1.5;A DMT-Based Arbitrary-Domain Theory;622
7.1.6;Summary;644
7.2;Vorticity and Vortices in Geophysical Flows;646
7.2.1;Governing Equations and Approximations;647
7.2.2;Potential Vorticity;657
7.2.3;Quasigeostrophic Evolution of Vorticity and Vortices;669
7.2.4;Summary;695
7.3;A Vectors, Tensors, and Their Operations;697
7.3.1;Vectors and Tensors;697
7.3.2;Integral Theorems and Derivative Moment Transformation;702
7.3.3;Curvilinear Frames on Lines and Surfaces;709
7.3.4;Applications in Lagrangian Description;720
8;References;724
9;Index;770