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Preface; Acknowledgments; Contents; 1 Fundamentals of Fluid Dynamics; 1.1 Basic Fluid Kinematics; 1.1.1 Description and Visualization of Fluid Motion; 1.1.2 Dilatation and Vorticity; 1.1.3 Velocity Gradient and Its Decompositions; 1.1.4 Local and Global Material Derivatives; 1.2 Dynamic Equations of Fluid Motion; 1.2.1 Dynamic Equations for General Fluids; 1.2.2 Constitutive Relations and Thermodynamics; 1.2.3 Navier-Stokes Equations and Perfect Gas; 1.2.4 Dominant Non-dimensional Parameters; 1.3 Wall-Bounded Flows; 1.3.1 Boundary Conditions; 1.3.2 Fluid Reaction to Solid Boundaries
1.4 Problems for Chapter 12 Fundamental Processes in Fluid Motion; 2.1 Preliminary Observations; 2.2 Intrinsic Decomposition of Fundamental Processes; 2.2.1 Helmholtz Decomposition; 2.2.2 Dynamic Equations for Vorticity and Dilatation; 2.3 Coupling and Splitting of Fundamental Processes; 2.3.1 Process Nonlinearity and Coupling Inside the Flow; 2.3.2 Process Linear Coupling on Boundaries; 2.3.3 Linearized Process Splitting in Unbounded Space; 2.4 Far-Field Asymptotics in Unbounded Flow; 2.4.1 Vorticity and Dilatation Far Fields; 2.4.2 Velocity Far Field
2.4.3 Far-Field Asymptotics for Steady Flow2.5 A Decoupled Model Flow: Inviscid Gas Dynamics; 2.5.1 Basic Equations; 2.5.2 Unsteady Potential Flows; 2.5.3 Steady Isentropic Flow; 2.6 Minimally-Coupled Model: Incompressible Flow; 2.6.1 Momentum Formulation versus Vorticity Formulation; 2.6.2 Incompressible Potential Flow; 2.6.3 Accelerated Body Motion and Virtual Mass; 2.6.4 Force on a Body in Steady Flow; 2.7 Problems for Chapter 2; 3 Vorticity Dynamics; 3.1 Kinematic Properties of Vorticity Field; 3.1.1 Vorticity Tube and Circulation; 3.1.2 Geometric Relation of Velocity and Vorticity
3.1.3 Two-Dimensional and Axisymmetric Vortical Flows3.1.4 Biot-Savart Formulas; 3.2 Vorticity Kinetic Vector and Circulation-Preserving Flow; 3.2.1 General Evolution Formulas; 3.2.2 Local Material Invariants; 3.2.3 Vorticity-Tube Stretching and Tilting; 3.2.4 Bernoulli Integrals; 3.3 Vorticity Integrals and Their Invariance; 3.3.1 Total Vorticity and Circulation; 3.3.2 Lamb-Vector Integrals; 3.3.3 Vortical and Potential Impulses; 3.3.4 Helicity; 3.3.5 Total Kinetic Energy; 3.4 Physical Causes of Vorticity Kinetics; 3.4.1 Coriolis Force in Rotating Fluid; 3.4.2 Baroclinicity
3.4.3 Vorticity Diffusion and Enstrophy Dissipation3.4.4 Vorticity Creation at Boundary; 3.5 Problems for Chapter 3; 4 Attached and Free Vortex Layers; 4.1 Parallel Shear Flows on Upper-Half Plane; 4.1.1 General Solution in Vorticity Formulation; 4.1.2 Singular BVF: Stokes First Problem (Rayleigh Problem); 4.1.3 Oscillatory BVF: Stokes Second Problem; 4.2 Boundary Layers: Formulation and Physics; 4.2.1 From d'Alembert's Paradox to Prandtl's Theory; 4.2.2 From Rayleigh Problem to Boundary Layer Equations; 4.2.3 Blasius Boundary Layers; 4.2.4 Further Issues
1.4 Problems for Chapter 12 Fundamental Processes in Fluid Motion; 2.1 Preliminary Observations; 2.2 Intrinsic Decomposition of Fundamental Processes; 2.2.1 Helmholtz Decomposition; 2.2.2 Dynamic Equations for Vorticity and Dilatation; 2.3 Coupling and Splitting of Fundamental Processes; 2.3.1 Process Nonlinearity and Coupling Inside the Flow; 2.3.2 Process Linear Coupling on Boundaries; 2.3.3 Linearized Process Splitting in Unbounded Space; 2.4 Far-Field Asymptotics in Unbounded Flow; 2.4.1 Vorticity and Dilatation Far Fields; 2.4.2 Velocity Far Field
2.4.3 Far-Field Asymptotics for Steady Flow2.5 A Decoupled Model Flow: Inviscid Gas Dynamics; 2.5.1 Basic Equations; 2.5.2 Unsteady Potential Flows; 2.5.3 Steady Isentropic Flow; 2.6 Minimally-Coupled Model: Incompressible Flow; 2.6.1 Momentum Formulation versus Vorticity Formulation; 2.6.2 Incompressible Potential Flow; 2.6.3 Accelerated Body Motion and Virtual Mass; 2.6.4 Force on a Body in Steady Flow; 2.7 Problems for Chapter 2; 3 Vorticity Dynamics; 3.1 Kinematic Properties of Vorticity Field; 3.1.1 Vorticity Tube and Circulation; 3.1.2 Geometric Relation of Velocity and Vorticity
3.1.3 Two-Dimensional and Axisymmetric Vortical Flows3.1.4 Biot-Savart Formulas; 3.2 Vorticity Kinetic Vector and Circulation-Preserving Flow; 3.2.1 General Evolution Formulas; 3.2.2 Local Material Invariants; 3.2.3 Vorticity-Tube Stretching and Tilting; 3.2.4 Bernoulli Integrals; 3.3 Vorticity Integrals and Their Invariance; 3.3.1 Total Vorticity and Circulation; 3.3.2 Lamb-Vector Integrals; 3.3.3 Vortical and Potential Impulses; 3.3.4 Helicity; 3.3.5 Total Kinetic Energy; 3.4 Physical Causes of Vorticity Kinetics; 3.4.1 Coriolis Force in Rotating Fluid; 3.4.2 Baroclinicity
3.4.3 Vorticity Diffusion and Enstrophy Dissipation3.4.4 Vorticity Creation at Boundary; 3.5 Problems for Chapter 3; 4 Attached and Free Vortex Layers; 4.1 Parallel Shear Flows on Upper-Half Plane; 4.1.1 General Solution in Vorticity Formulation; 4.1.2 Singular BVF: Stokes First Problem (Rayleigh Problem); 4.1.3 Oscillatory BVF: Stokes Second Problem; 4.2 Boundary Layers: Formulation and Physics; 4.2.1 From d'Alembert's Paradox to Prandtl's Theory; 4.2.2 From Rayleigh Problem to Boundary Layer Equations; 4.2.3 Blasius Boundary Layers; 4.2.4 Further Issues