David Tong: Lectures on Fluid Mechanics
These lecture notes provide a introduction to fluid mechanics, aimed at undergraduates. The full set of lecture notes come in around 240 pages and can be downloaded here. Please do email me if you find any typos or corrections.
Content
- 1. Introduction and Inviscid Flows:
PDF
Introduction; path lines and streamlines; the material time derivative; conservation of mass; the stream function. The Euler equation; Archimedes principle; Bernoulli's principle. Vorticity and Kelvin's circulation theorem. Potential flows; D'Alembert's paradox; circulation, lift and the Magnus force. An action principle for fluids. - 2. The Navier-Stokes Equation:
PDF
Stress, Strain and viscosity; Newtonian fluids; dissipation. The no-slip boundary condition; Couette flow; Poiseuille flow; Vorticity and the Burgers vortex. Reynolds number. Stokes flow; Stokes' drag law; Moffat eddies; Swimming at low Reynolds number; Hele-Shaw flow. The boundary layer, Prandtl's equation; Blasius' solution; Falkner-Scan boundary layers; separation. - 3. Waves: PDF
Surface waves; free boundary conditions; surface tension and capillary waves. Gravity waves. Shallow water waves, geostrophic balance, Poincare waves, Coastal Kelvin waves, Equatorial waves including Rossby waves, Yanai waves and Kelvin waves, topologically protected waves. Sound waves; compressible fluids; heat transport and thermodynamics; viscosity and damping. Non-linear sound waves; the method of characteristiscs; wave steepening; Burgers' equation. Shocks; supersonic flows; Rankine-Huginiot jump conditions and relations. - 4. Instabilities:
PDF
Kevlin-Helmsholtz instability; the vortex sheet; Rayleigh-Taylor instability. Rayleigh-Plateau instability. Rayleigh-Benard convection; the Boussinesq approximation. Instabilities of shear flows; Rayleigh's criterion; Fjortoft's criterion; the semi-circle theorem. - 5. Turbulence:
PDF
Mean flow; Reynolds averaging and the Reynolds-averaged Navier Stokes equation; Reynolds stress and eddy viscosity. Kolmogorov's dimensional analysis (K41). Velocity correlation functions and structure functions, the von Karman relation and the von Karman-Howarth relation. Kolmogorov's 4/5's law.
Fluids on the Web
- Michael McIntyre's fluid mechanics roadshow.
- Fluid Mechanics II by John Hinch, University of Cambridge.
- Fluids by Caroline Terquem, University of Oxford.
- Fluid Dynamics by Stephen Childress, NYU
- Waves by Stephen Cowley, University of Cambridge.
- Advanced Fluid Dynamics by Chiang Mei, MIT.
- Advanced Fluid Dynamics by Lennon O'Naraigh, University College Dublin (focussing on hydrodynamic stability).
Some Classic Papers
- Osborne Reynolds' classic paper from 1883
- Prandtl's original paper on the boundary layer. (In German.)
- Swimming at Low Reynolds Number by Ed Purcell