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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 | |