1. Introduction
1.1 Preliminaries
1.2 Differential Equations， Initial and Boundary Conditions
1.3 Major Assumptions
1.4 Vorticity—Dynamic Formulation
References
2. Theorems of Helmholtz and Kelvin
2.1 Introduction
2.2 Kinematic—Kinetic Partition of Flow Problem
2.3 Kinematic Preliminaries
2.4 Helmholtz' First Vortex Theorem
2.5 Vorticity Loops
2.6 Kelvin's Theorem
2.7 Helmholtz' Second Vortex Theorem
2.8 Concluding Remarks
References
3. Vorticity Kinematics
3.1 Differential Equations of Vorticity Kinematics
3.2 Vector Identities
3.3 Poisson's Equation and Integral Representations
3.4 Poisson's Equation and Boundary Conditions
3.5 Law of Biot—Savart
3.6 Generalized Law of Biot—Savart
3.7 Uniqueness of Solution
3.8 Boundary Conditions in Vorticity Kinematics
References
4. Vorticity Kinetics
4.1 Navier—Stokes Momentum Equation
4.2 Convection and Material Derivative
4.3 Viscous Force and Diffusion of Momentum
4.4 Vorticity and Flow Regions
4.5 Appearance and Transport of Vorticity
4.6 Speeds of Vorticity Transport
4.7 Boundary Conditions in Vorticity Kinetics
4.8 Approaching Steady Flow
References
5. Vorticity—Moment Theorem
5.1 Preliminary Remarks
5.2 Total Vorticity Conservation
5.3 Asymptotic Behavior of Velocity Field
5.4 Total Velocity
5.5 Aerodynamic Force
5.6 Moment of Aerodynamic Force
5.7 Two—Dimensional Flows
5.8 Observations
References
6. Classical Aerodynamics
6.1 Vorticity—Moment Theorem
6.2 Kutta—Joukowski's Theorem and Vortical Flow Zones
6.3 Non—Streamlined Flow and Karman Vortex Street
6.4 Vorticity Loop and Vorticity Moment
6.5 Lifting—Line Theory： Uniform Circulation Lift
6.6 Lift on Finite Wing with Variable Circulation
6.7 Induced Drag
6.8 Wake—Integral Expressions for Lift and Drag
References
7. Unsteady Aerodynamics
7.1 Aircraft and Streamlined Flows
7.2 Animal Flight and Flapping Wings
7.3 Classical vs. Vorticity—Dynamic Approach
7.4 Apparent Mass of Sphere and Circular Disk
7.5 Apparent Mass Coefficients
References
Index
