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| Preface | |
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| Equations of Motion | |
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| The fluid state | |
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| The material derivative | |
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| Conservation of mass: Equation of continuity | |
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| Momentum equation | |
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| Relative motion of neighbouring fluid elements | |
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| Viscous stress tensor | |
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| Navier-Stokes equation | |
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| The Reynolds equation and Reynolds stress | |
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| The energy equation | |
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| Alternative treatment of the energy equation | |
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| Energy equation for incompressible flow | |
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| Summary of governing equations | |
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| Boundary conditions | |
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| Potential Flow of an Incompressible Fluid | |
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| Ideal fluid | |
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| Kelvin's circulation theorem | |
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| The velocity potential | |
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| Bernoulli's equation | |
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| Impulsive pressure | |
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| Streamlines and intrinsic equations of motion | |
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| Bernoulli's equation in steady flow | |
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| Motion produced by a pulsating sphere | |
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| The point source | |
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| Free-space Green's function | |
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| Monopoles, dipoles, and quadrupoles | |
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| The vibrating sphere | |
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| Streamlines | |
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| Far field of a monopole distribution of zero strength | |
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| Green's formula | |
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| Volume and surface integrals | |
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| Green's formula | |
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| Sources adjacent to a plane wall | |
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| Determinancy of the motion | |
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| Fluid motion expressed in terms of monopole or dipole distributions | |
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| Determinancy of cyclic irrotational flow | |
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| Kinetic energy of cyclic irrotational flow | |
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| The kinetic energy | |
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| Converse of Kelvin's minimum-energy theorem | |
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| Energy of motion produced by a translating sphere | |
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| Problems with spherical boundaries | |
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| Legendre polynomials | |
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| Velocity potential of a point source in terms of Legendre polynomials | |
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| Interpretation in terms of images | |
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| The Stokes stream function | |
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| Stream function examples | |
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| Rankine solids | |
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| Rankine ovoid | |
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| Drag in ideal flow | |
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| Axisymmetric flow from a nozzle | |
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| Irrotational flow from a circular cylinder | |
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| Borda's mouthpiece | |
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| The incompressible far field | |
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| Deductions from Green's formula | |
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| Far field produced by motion of a rigid body | |
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| Inertia coefficients | |
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| Pressure in the far field | |
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| Force on a rigid body | |
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| Moment exerted on a rigid body | |
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| Sources near solid boundaries | |
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| The reciprocal theorem | |
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| Far-field Green's function | |
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| The Kirchhoff vector | |
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| Far-field Green's function for a sphere | |
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| Far-field Green's function for cylindrical bodies | |
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| The circular cylinder | |
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| The rigid strip | |
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| Symmetric far-field Green's function | |
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| Far field of an arbitrarily moving body | |
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| Far-field Green's function summary and special cases | |
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| General form | |
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| Airfoil of variable chord | |
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| Projection or cavity on a plane wall | |
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| Rankine ovoid | |
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| Circular aperture | |
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| Circular disc | |
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| Ideal Flow in Two Dimensions | |
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| Complex representation of fluid motion | |
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| The stream function | |
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| The complex potential | |
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| Uniform flow | |
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| Flow past a cylindrical surface | |
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| The circular cylinder | |
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| Circle theorem | |
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| Uniform flow past a circular cylinder | |
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| The line vortex | |
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| Circular cylinder with circulation | |
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| Equation of motion of a cylinder with circulation | |
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| The Blasius force and moment formulae | |
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| Blasius's force formula for a stationary rigid body | |
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| Blasius's moment formula for a stationary rigid body | |
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| Kutta-Joukowski lift force | |
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| Leading-edge suction | |
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| Sources and line vortices | |
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| Line vorrtices | |
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| Motion of a line vortex | |
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| Karman vortex street | |
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| Kinetic energy of a system of rectilinear vortices | |
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| Conformal transformations | |
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| Transformation of Laplace's equation | |
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| Equation of motion of a line vortex | |
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| Numerical integration of the vortex path equation | |
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| The Schwarz-Christoffel transformation | |
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| Irrotational flow from an infinite duct | |
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| Irrotational flow through a wall aperture | |
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| Free-streamline theory | |
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| Coanda edge flow | |
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| Mapping from the w plane to the t plane | |
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| Separated flow through an aperture | |
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| The wake of a flat plate | |
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| Flow past a curved boundary | |
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| The hodograph transformation formula | |
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| Chaplygin's singular point method | |
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| Jet produced by a point source | |
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| Deflection of trailing-edge flow by a source | |
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| The Joukowski transformation | |
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| The flat-plate airfoil | |
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| Calculation of the lift | |
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| Lift calculated from the Kirchhoff vector force formula | |
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| Lift developed by a starting airfoil | |
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| The Joukowski airfoil | |
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| Streamline flow past an airfoil | |
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| Separation and stall | |
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| Linear theory of separation | |
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| Sedov's method | |
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| Boundary conditions | |
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| Sedov's formula | |
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| Tandem airfoils | |
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| High-lift devices | |
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| Plain flap or aileron | |
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| Point sources and vortices | |
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| Flow through a cascade | |
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| Unsteady thin-airfoil theory | |
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| The vortex sheet wake | |
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| Translational oscillations | |
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| The unsteady lift | |
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| Leading-edge suction force | |
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| Energy dissipated by vorticity production | |
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| Hankel function formulae | |
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| Rotational Incompressible Flow | |
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| The vorticity equation | |
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| Vortex lines | |
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| Vortex tubes | |
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| Movement of vortex lines: Helmholtz's vortex theorem | |
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| Crocco's equation | |
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| Convection and diffusion of vorticity | |
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| Vortex sheets | |
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| The Biot-Savart law | |
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| The far field | |
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| Kinetic energy | |
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| The Biot-Savart formula in the presence of an internal boundary | |
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| The Biot-Savart formula for irrotational flow | |
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| Examples of axisymmetric vortical flow | |
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| Circular vortex filament | |
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| Rate of production of vorticity at a nozzle | |
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| Blowing out a candle | |
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| Axisymmetric steady flow of an ideal fluid | |
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| Hill's spherical vortex | |
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| Some viscous flows | |
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| Diffusion of vorticity from an impulsively started plane wall | |
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| Diffusion of vorticity from a line vortex | |
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| Creeping flow | |
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| Motion of a sphere at very small Reynolds number | |
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| The Oseen approximation | |
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| Laminar flow in a tube (Hagen-Poiseuille flow) | |
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| Boundary layer on a flat plate; Karman momentum integral method | |
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| Force on a rigid body | |
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| Surface force in terms of the impulse | |
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| The Kirchhoff vector force formula | |
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| The Kirchhoff vector force formula for irrotational flow | |
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| Arbitrary motion in a viscous fluid | |
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| Body moving without rotation | |
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| Surface force in two dimensions | |
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| Bluff body drag at high Reynolds number | |
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| Modelling vortex shedding from a sphere | |
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| Force and impulse in fluid of non-uniform density | |
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| Integral identities | |
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| Surface moment | |
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| Moment for a non-rotating body | |
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| Airfoil lift, drag, and moments | |
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| Vortex-surface interactions | |
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| Pressure expressed in terms of the total enthalpy | |
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| Equation for B | |
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| Solution of the B equation | |
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| The far field | |
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| Surface Gravity Waves | |
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| Introduction | |
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| Conditions at the free surface | |
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| Wave motion within the fluid | |
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| Linearised approximation | |
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| Time harmonic, plane waves on deep water | |
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| Water of finite depth | |
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| Surface wave energy | |
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| Wave-energy density | |
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| Wave-energy flux | |
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| Group velocity | |
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| Viscous damping of surface waves | |
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| The interior damping | |
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| Boundary-layer damping | |
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| Comparison of boundary-layer and internal damping for long waves | |
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| Shallow-water waves | |
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| Waves on water of variable depth | |
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| Shallow-water Green's function | |
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| Waves generated by a localised pressure rise | |
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| Waves approaching a sloping beach | |
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| Method of stationary phase | |
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| Formulation of initial-value dispersive-wave problems | |
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| Evaluation of Fourier integrals by the method of stationary phase | |
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| Numerical results for the surface displacement | |
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| Conservation of energy | |
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| Rayleigh's proof that energy propagates at the group velocity | |
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| Surface wave-energy equation | |
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| Waves generated by a submarine explosion | |
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| Initial-value problems in two surface dimensions | |
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| Waves generated by a surface elevation symmetric about the origin | |
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| The energy equation in two dimensions | |
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| Surface motion near a wavefront | |
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| One-dimensional waves | |
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| Waves generated by motion of the seabed | |
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| Tsunami produced by an undersea earthquake | |
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| Periodic wave sources | |
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| One-dimensional waves | |
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| Periodic sources in two surface dimensions | |
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| The surface wave power | |
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| Surface wave amplitude | |
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| Ship waves | |
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| Moving line pressure source | |
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| Wave-making resistance | |
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| Moving point-like pressure source | |
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| Plotting the wave crests | |
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| Behaviour at the caustic | |
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| Wave-making power | |
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| Wave amplitude calculated from the power | |
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| Ray theory | |
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| Kinematic theory of wave crests | |
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| Ray tracing in an inhomogeneous medium | |
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| Refraction of waves at a sloping beach | |
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| Wave action | |
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| Variational description of a fully dispersed wave group | |
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| Fully dispersed waves in a non-uniformly moving medium | |
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| General wave-bearing media | |
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| Diffraction of surface waves by a breakwater | |
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| Diffraction by a long, straight breakwater | |
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| Solution of the diffraction problem | |
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| The surface wave pattern | |
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| Uniform asymptotic approximation: Method of steepest descents | |
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| Introduction to Acoustics | |
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| The wave equation | |
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| The linear wave equation | |
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| Plane waves | |
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| Speed of sound | |
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| Acoustic Green's function | |
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| The impulsive point source | |
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| Green's function | |
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| Retarded potential | |
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| Sound from a vibrating sphere | |
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| Acoustic energy flux | |
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| Green's function in one space dimension: Method of descent | |
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| Waves generated by a one-dimensional volume source | |
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| Kirchhoff's formula | |
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| Compact Green's function | |
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| Generalized Kirchhoff formula | |
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| The time harmonic wave equation | |
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| The compact approximation | |
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| Rayleigh scattering: Scattering by a compact body | |
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| One-dimensional propagation through junctions | |
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| Continuity of volume velocity | |
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| Continuity of pressure | |
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| Reflection and transmission at a junction | |
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| Branching systems | |
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| Fundamental formula | |
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| Energy transmission | |
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| Acoustically compact cavity | |
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| The Helmholtz resonator | |
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| Acoustic filter | |
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| Admittance of a narrow constriction | |
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| Radiation from an open end | |
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| Rayleigh's method for low-frequency sound | |
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| The reflection coefficient | |
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| Admittance of the open end | |
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| Open-end input admittance | |
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| Flanged opening | |
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| Physical significance of the end correction | |
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| Admittance of a circular aperture | |
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| Webster's equation | |
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| Radiation into a semi-infinite duct | |
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| The compact Green's function | |
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| Wave generation by a train entering a tunnel | |
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| Damping of sound in a smooth-walled duct | |
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| Time harmonic propagation in a duct | |
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| The viscous contribution | |
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| The thermal contribution | |
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| The thermo-viscous damping coefficient | |
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| Bibliography | |
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| Index | |