Signal Speeds in Fluids

Surface and Internal Waves, Sound, Nozzles and Shocks in 9 chapters — from “Waves of finite height: Stokes waves, shoaling and breaking” to “Oblique shocks, expansion fans and blast waves”.

Chapters

  1. Waves of finite height: Stokes waves, shoaling and breaking
    • The Stokes expansion to second order
    • Amplitude dispersion of steep waves
    • Stokes drift and the mass transport of swell
    • The limiting wave height and breaking
    • Viscous wave damping and oil films
    • Wave shoaling on a sloping beach
    • Depth refraction and the turning of crests
    • Radiation stress, set-down and set-up
    • Limits of the Stokes expansion
    • Problems
  2. Long waves of finite height: bores, jumps and solitary waves
    • Characteristics of a first-order wave equation
    • The shallow-water equations from a slab
    • Riemann invariants and characteristics
    • Simple waves and long-wave steepening
    • Dam-break flow
    • Specific energy and critical depth
    • The hydraulic jump
    • Tidal bores and the surf-zone bore
    • The solitary wave and the Ursell number
    • What the shallow-water equations settle
    • Problems
  3. Internal gravity waves in a stratified fluid
    • Interfacial waves between two layers
    • The Boussinesq equations for a stratified fluid
    • The internal wave dispersion relation
    • Internal wave group velocity along the crests
    • The St Andrew's cross from an oscillating cylinder
    • Internal wave reflection and the critical slope
    • Lee waves behind a mountain ridge
    • Vertical modes of a stratified ocean
    • The internal wave dispersion relation at tidal periods
    • Problems
  4. Waves in a rotating fluid: inertial, Poincare and Kelvin waves
    • Euler's equation in a rotating frame
    • Inertial oscillations on a rotating Earth
    • Inertial waves in a rotating tank
    • The Taylor column as a wave effect
    • Inertia-gravity waves and the internal tide
    • Poincare waves in a rotating shallow sea
    • The deformation radius
    • Kelvin waves along a coast
    • Geostrophic adjustment of a step
    • What the deformation radius settles
    • Problems
  5. Sound in a moving, absorbing fluid: sources, refraction and loss
    • The acoustic energy equation
    • The convected wave equation
    • Sound refraction by wind and temperature
    • Acoustic multipoles and compact sources
    • Lighthill's acoustic analogy and jet noise
    • Classical absorption by viscosity and conduction
    • Relaxation absorption in air and sea water
    • Acoustic streaming and radiation force
    • What the acoustic energy equation settles
    • Problems
  6. Steady compressible flow: energy, stagnation and the Mach number
    • The compressible Euler equations
    • The steady-flow energy equation
    • The stagnation state and the compressible Pitot tube
    • The sonic state and the limiting speed
    • The Prandtl-Glauert rule for subsonic flow
    • Mach waves in a supersonic stream
    • Supersonic thin-aerofoil theory and wave drag
    • What the sonic state leaves open
    • Problems
  7. Flow through nozzles: area change, choking and thrust
    • Mass flux at the sonic state
    • Quasi-one-dimensional flow in a channel
    • The area-velocity relation
    • The area-Mach relation
    • Choked mass flow and the sonic throat
    • The converging nozzle and back pressure
    • The de Laval nozzle and its regimes
    • Rocket thrust and specific impulse
    • Fanno and Rayleigh flows
    • What the de Laval nozzle settles
    • Problems
  8. Steepening and the normal shock wave
    • What a hydraulic jump conserves
    • Gas-dynamic characteristics and simple waves
    • Shock formation in a loud sound wave
    • The Rankine-Hugoniot conditions
    • The normal shock relations
    • The entropy jump and the second law
    • Shock thickness and the limits of the continuum
    • The shock tube
    • The hydraulic analogy
    • The nozzle shock at off-design back pressure
    • What the normal shock relations settle
    • Problems
  9. Oblique shocks, expansion fans and blast waves
    • Normal shock relations in a sliding frame
    • The oblique shock on a wedge
    • The detached bow shock and supersonic Pitot tubes
    • The Prandtl-Meyer expansion fan
    • Shock-expansion theory for a flat plate
    • Shock reflection at a wall
    • Shock diamonds in off-design jets
    • The blast wave from a point explosion
    • What oblique shocks and blast waves settle
    • Problems