Chapter 1: Kinematics of a Flow
1.1: Fluid velocity and motion of fluid parcels
1.2: Lagrangian labels
1.3: Properties of parcels, conservation of mass, and the continuity equation
1.4: Material lines, material vectors, and material surfaces
1.5: Differential geometry of surfaces
1.6: Description of a material surface in Eulerian form
1.7: Streamlines, stream tubes, path lines, and streak lines
1.8: Vorticity, vortex lines, vortex tubes, and circulation around loops
1.9: Line vortices and vortex sheets
Chapter 2: Analysis of Kinematics
2.1: Irrotational flows and the velocity potential
2.2: The reciprocal relation for harmonic functions, and Green's functions of Laplace's equation
2.3: Integral representation and further properties of potential flow
2.4: The vector potential for incompressible flow
2.5: Representation of an incompressible flow in terms in the vorticity
2.6: Representation of a flow in terms of the rate of expansion and vorticity
2.7: Stream functions for incompressible flow
2.8: Flow induced by vorticity
2.9: Axisymmetric flow induced by vorticity
2.10: Two-dimensional flow induced by vorticity
Chapter 3: Stresses, the Equation of Motion, and the Vorticity Transport Equation
3.1: Forces acting in a fluid, traction, the stress tensor, and the equation of motion
3.2: Constitutive relations for the stress tensor
3.3: Traction, force, torque, energy dissipation, and the reciprocal theorem for incompressible Newtonian fluids
3.4: Navier-Stokes', Euler's and Bernoulli's equation
3.5: Equations and boundary conditions governing the motion of an incompressible Newtonian fluid
3.6: Traction, vorticity, and flow kinematics on rigid boundaries, free surfaces, and fluid interfaces
3.7: Scaling of the Navier-Stokes equation and dynamic similtude
3.8: Evolution of circulation around material loops and dynamics of the vorticity field
3.9: Computation of exact solutions to the equation of motion in two dimensions based in the vorticity transport equation
Chapter 4: Hydrostatics
4.1: Pressure distribution within a fluid in rigid body motion
4.2: The Laplace-Young equation
4.3: Two-dimensional interfaces
4.4: Axisymmetric interfaces
4.5: Three-dimensional interfaces
Chapter 5: Computing Incompressible Flows
5.1: Steady unidirectional flows
5.2: Unsteady unidirectional flows
5.3: Stagnation-point flows
5.4: Flow due to a rotating disk
5.5: Flow in a corner due to a point source
5.6: Flow due to a point force
Chapter 6: Flow at Low Reynolds Numbers
6.1: Equations and fundamental properties of Stokes flow
6.2: Local solutions in corners
6.3: Nearly-unidirectional flows
6.4: Flow due to a point force
6.5: Fundamental solutions of Stokes flow
6.6: Stokes flow past or due to the motion of rigid bodies and liquid drops
6.7: Computation of singularity representations
6.8: The Lorentz reciprocal theorem and its applications
6.9: Boundary integral representation of Stokes flows
6.10: Boundary-integral-equation methods
6.11: Generalized Faxen's relations
6.12: Formulation of two-dimensional Stokes flow in complex variables
6.13: Effects of inertia and Oseen flow
6.14: Unsteady Stokes flow
6.15: Computation of unsteady Stokes flow past or due to the motion of particles
Chapter 7: Irrotational Flow
7.1: Equations and computation of irrotational flow
7.2: Flow past or due to the motion of three-dimensional body
7.3: Force and torque exerted on a three-dimensional body
7.4: Flow past or due to the motion of a sphere
7.5: Flow past or due to the motion of non-spherical bodies
7.6: Flow past of due to the motion of two-dimensional bodies
7.7: Computation of two-dimensional flow past or due to the motion of a body
7.8: Formulation of two-dimensional flow in complex variables
7.9: Conformal mapping
7.10: Applications of conformal mapping to flow past two-dimesensional bodies
7.11: The Schwarz-Christoffel transformation and its applications
Chapter 8: Boundary Layers
8.1: Boundary-layer theory
8.2: The boundary layer on a semi-infinite flat plate
8.3: Boundary layers in acclerating and decelerating flow
8.4: Computation of boundary layers around two-dimensional bodies
8.5: Boundary layers in axisymmetric and three-dimensional flows
8.6: Unsteady boundary layers
Chapter 9: Hydrodynamic Stability
9.1: Evolution equations and forumulation of the linear stability problem
9.2: Solution of the initial-value problem and normal-mode analysis
9.3: Normal-mode analysisof unidirectional flows
9.4: General theorems of the temporal stability of inviscid shear flows
9.5: Stability of a uniform layer subject to spatially periodic disturbances
9.6: Numerical solution of the Orr-Sommerfeld and Rayleigh equations
9.7: Stability of certain classes of unidirectional flows
9.8: Stability of a planar interface in potential flow
9.9: Viscous interfacial flows
9.10: Capillary instability of a curved interface
9.11: Inertial instability of rotating fluids
Chapter 10: Boundary-Integral Methods for Potential Flow
10.1: The boundary-integral equation
10.2: Boundary-element methods
10.3: Generalized boundary-integral representations
10.4: The single-layer potential
10.5: The double-layer potential
10.6: Investigation of integral equations of the second kind
10.7: Regularization of integral equations of the second kind
10.8: Completed double-layer representation for exterior flow
10.9: Iterative solution of integral equations of the second kind
Chapter 11: Vortex Motion
11.1: Invariants of the motion
11.2: Point vortices
11.3: Vortex blobs
11.4: Two-dimensional vortex sheets
11.5: Two-dimensional flows with distributed vorticity
11.6: Two-dimensional vortex patches
11.7: Axisymmetric flow
11.8: Three-dimensional flow
Chapter 12: Finite-Difference Methods for the Convection-Diffusion Equation
12.1: Definitions and procedures
12.2: One-dimensional diffusion
12.3: Diffusion in two and three dimensions
12.4: One-dimensional convection
12.5: Convection in two and three dimensions
12.6: Convection-diffusion in one dimension
12.7: Convection-diffusion in two and three dimensions
Chapter 13: Finite-Difference Methods for Incompressible Newtonian Flow
13.1: Methods based on the vorticity transport equation
13.2: Velocity-pressure formulation
13.3: Implementation of methods in primitive variables
13.4: Operator splitting, projection, and pressure-correction methods
13.5: Methods of modified dynamics or false transients
Appendix A: Index Notation, Differential Operators, and Theorems of Vector Calculus
A.1: Index Notation
A.2: Vector and matrix products, differential operators in Cartesian coordinates
A.3: Orthogonal curvilinear coordinates
A.4: Differential operators in cylindrical and plane polar coordinates
A.5: Differential operators in spherical polar coordinates
A.6: Integral theorems of vector calculus
Appendix B: Primer of Numerical Methods
B.1: Linear algebra equations
B.2: Computation of eigenvalues
B.3: Nonlinear algebraic equations
B.4: Function interpolation
B.5: Computation of derivatives
B.6: Function integration
B.7: Function approximation
B.8: Integration of ordinary differential equations
B.9: Computation of special functions
