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

This book is a comprehensive and intensive monograph for scientists, engineers and applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief review of fundamentals of fluid dynamics, with an innovative emphasis on the intrinsic orthogonal decomposition of fluid dynamics process. This is followed by vortex dynamics dealing with the motion, interaction, stability, and breakdown of various vortices. Typical vortex structures are analyzed in laminar, translational, and turbulent flows, including stratified and rotational fluids. In another chapter vortical flow management is presented, such as diagnostics and control. Physical understanding of vortical flow phenomena and mechanisms is the first priority throughout the book. To make the book self-contained, some mathematical background is briefly presented in the main text, but major prerequisites are systematically given in appendices.

Autoren/Hrsg.

Wu, Jie-Zhi

Ma, Hui-Yang

Zhou, Ming-De

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