Vorticity and Vortex Dynamics (eBook)

Preface 5
Contents 7
Introduction 15
Fundamental Processes in Fluid Dynamics and Their Coupling 16
Historical Development 17
The Contents of the Book 20
Vorticity Dynamics 24
Fundamental Processes in Fluid Motion 25
Basic Kinematics 25
Fundamental Equations of Newtonian Fluid Motion 37
Intrinsic Decompositions of Vector Fields 48
Splitting and Coupling of Fundamental Processes 60
Summary 75
Vorticity Kinematics 78
Physical Interpretation of Vorticity 78
Vorticity Integrals and Far-Field Asymptotics 82
Lamb Vector and Helicity 96
Vortical Impulse and Kinetic Energy 105
Vorticity Evolution 111
Circulation-Preserving Flows 120
Summary 138
Fundamentals of Vorticity Dynamics 141
Vorticity Diffusion Vector 141
Vorticity Field at Small Reynolds Numbers 160
Vorticity Dynamics in Boundary Layers 171
Vortex Sheet Dynamics 182
Vorticity-Based Formulation of Viscous Flow Problem 195
Summary 209
Vorticity Dynamics in Flow Separation 211
Flow Separation and Boundary-Layer Separation 211
Three-Dimensional Steady Flow Separation 214
Steady Boundary Layer Separation 226
Unsteady Separation 244
Summary 261
Vortex Dynamics 263
Typical Vortex Solutions 264
Governing Equations 264
Axisymmetric Columnar Vortices 269
Circular Vortex Rings 281
Exact Strained Vortex Solutions 293
Asymptotic Strained Vortex Solutions 304
On the Definition of Vortex 319
Summary 329
Separated Vortex Flows 331
Topological Theory of Separated Flows 331
Steady Separated Bubble Flows in Euler Limit 347
Steady Free Vortex-Layer Separated Flow 360
Unsteady Bluff-Body Separated Flow 374
Summary 389
Core Structure, Vortex Filament, and Vortex System 391
Vortex Formation and Core Structure 391
Dynamics of Three-Dimensional Vortex Filament 407
Motion and Interaction of Multiple Vortices 426
Vortex–Boundary Interactions 442
Summary 454
Vortical Flow Instability, Transition and Turbulence 456
Vortical-Flow Stability and Vortex Breakdown 457
Fundamentals of Hydrodynamic Stability 457
Shear-Flow Instability 475
Instability of Axisymmetric Columnar Vortices 486
Instabilities of Strained Vortices 498
Vortex Breakdown 508
Summary 521
Vortical Structures in Transitional and Turbulent Shear Flows 525
Coherent Structures 526
Vortical Structures in Free Shear Flows 532
Vortical Structures in Wall-Bounded Shear Layers 541
Some Theoretical Aspects in Studying Coherent Structures 556
Two Basic Processes in Turbulence 567
Vortical Structures in Other Shear Flows 579
Summary 589
Special Topics 591
Vortical Aerodynamic Force and Moment 592
Introduction 592
Projection Theory 599
Vorticity Moments and Classic Aerodynamics 604
Boundary Vorticity-Flux Theory 613
A DMT-Based Arbitrary-Domain Theory 622
Summary 644
Vorticity and Vortices in Geophysical Flows 646
Governing Equations and Approximations 647
Potential Vorticity 657
Quasigeostrophic Evolution of Vorticity and Vortices 669
Summary 695
A Vectors, Tensors, and Their Operations 697
Vectors and Tensors 697
Integral Theorems and Derivative Moment Transformation 702
Curvilinear Frames on Lines and Surfaces 709
Applications in Lagrangian Description 720
References 724
Index 770