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Table of Contents
Preface
Chapter
1. Introduction
1. Role of
viscosity in high Reynolds number flows
2. Inviscid
flows
Chapter 2.
Vectors and Tensors
1. Cartesian
index notation
2. Kronecker
delta and permutation tensor
3. Vector and
tensor operations
4. Vector and
tensor transformations
5. Symmetric
and skew-symmetric tensors
6. Vector
identities
7. Integral
identities
Chapter 3.
Kinematics of Fluid Motion
1. Descriptions
of fluid motion
2. Deformation
measures
3.
Stretch rate and vorticity
4. Dilatation
5. Pathlines,
streaklines, streamlines and vortex lines
6. Transport
theorem
Chapter 4.
Laws of Fluid Dynamics
1. Mass
conservation
2. Momentum
conservation
3. Moment of
momentum conservation
4. Kinetic
energy transport theorem
5. Constraint
of incompressibility
6. Navier-Stokes
equation and some simple solutions
Chapter 5.
Dynamics of Discontinuity Surfaces
1. Extended
transport theorem for a region containing a
discontinuity surface
2. Jump
conditions across a surface of discontinuity
3. Surface
tension
4. Boundary
conditions for fluid flow
Chapter 6.
Velocity Representations and Associated Theorems
1. Irrotational (lamellar) and related flows
2. Incompressible (solenoidal) flows
3. Flows that are both incompressible and irrotational
4. Helmholtz representation theorem
5. Biot-Savart law
6. Far-field asymptotic form for velocity in a flow
extending to infinity
Chapter 7.
Vorticity Transport Theorems
1. Vorticity
transport equation
2. Motion
of vortex lines
3. Preservation
of circulation
4. Vorticity
measures and invariants
5. Vorticity
invariants in two-dimensional flows
6. Vorticity
transport and invariants in viscous flows
Chapter 8.
Pressure Theorems
1. Pressure
Poisson equation
2. Bernoulli
theorem
3. Boundary
integral equation for pressure
4. Special
results for steady, two-dimensional flows
Chapter 9.
Two-Dimensional Potential Flows
1. Analogy
between potential flows and analytic functions of a complex
variable
2. Some basic
potential flows
3. Superposition
of basic flows
4. Circle
theorem
5. Method
of images
6. Conformal
transformation of fluid flows
7. Transformation
8. Joukowski
transformation
9. Schwarz-Christoffel
equation
10. Free streamline
theory
Chapter 10.
Forces on Bodies in Two-Dimensional Flows
1. Integration
in the complex plane
2. Blasius
force and moment laws
3. Lagally’s
theorem
4. D'Alembert's
paradox and the Kutta-Joukowski lift law
5. Application
to two-dimensional airfoils
Chapter 11.
Two-Dimensional Flows With Vorticity
1.
Systems of point vortices
2.
Schwarz function approach for uniform vorticity patches
3.
Contour integration method for uniform vorticity patches
4.
Discrete vortex numerical methods: Basic method
5.
Discrete vortex numerical methods: Acceleration techniques
6.
Vortex sheets
7. Vortex sheet representation of flat-plate airfoils
8. Flow
with uniform background vorticity
Chapter
12. Three-Dimensional
Potential Flows
1. Governing
equations
2. Basic
potential flows
3. Some
axisymmetric flows with immersed bodies
4. Sphere
theorems
5. Slender
body theory
6.
Source and doublet sheet boundary integral methods
7.
Vortex sheet boundary integral method
8. Forces
induced by singularities
9.
Added mass and buoyancy forces
Chapter 13.
Axisymmetric Vortex Flows
1. General
theory
2. Thin-core
vortex rings
3.
Hill's spherical vortex
4.
Axisymmetric contour dynamics
5.
Steady axisymmetric flows
6.
Waves of variable core area
7.
Plug-flow model
8. Axisymmetric
discrete vortex method
Chapter
14. Vortex Tubes
1. Velocity
field induced by a curved vortex filament
2. Cut-off
model for a vortex tube
3. Local-induction
approximation
4.
Bending waves on a vortex tube
Chapter 15.
Interfacial Wave Motion
1. Internal
waves in layered media
2.
Linear wave theory
3.
Capillary and gravity waves
4.
Particle displacement in a wave field
5. Wave
energy and group velocity
6. Boundary
integral method for nonlinear interfacial waves
Chapter 16.
Stability of Fluid Flows
1. General
concepts
2. Stability
of an elliptical vortex patch in a straining flow
3. Stability
of two-dimensional point vortex arrays
4. Interfacial
instabilities
5. Capillary
instability of a liquid jet
6. Centrifugal
instability
7. Stability
of parallel shear flows
8. Three-dimensional
instability of a vortex pair
Appendix. Common Expressions in Orthogonal
Curvilinear Coordinate Systems
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