Course description
Principles versus applications, utility of toy models (causation versus correlation). What is a fluid? Speed of sound versus speed of light. Dimensionless fluid numbers. Qualitative discussion of Rayleigh-Taylor instability. Imploding/exploding house and Bernoulli’s constant. Equations of mass, momentum and energy conservation, including derivation of stress tensor, discussion of Stokes’s assumption and Newtonian fluids. Watch movies of non-Newtonian fluids. Begin with movies showing examples of Rayleigh-Taylor and Kelvin-Helmholtz instabilities. Unified linear analysis for both. Use analysis to derive timescale for Rayleigh-Taylor instability. Analyze Kelvin-Helmholtz instability. Discuss role of surface tension. Thought experiments for convection: pot on stove versus the Earth. Concept of potential temperature and entropy. Schwarzschild’s criterion using potential density. Lapse rate and adiabatic lapse rate, including estimates for Earth. Mixing length theory. Convective adjustment. Movie of Rayleigh-Benard convection. Watch documentary on turbulence. Kolmogorov scaling laws. Reynolds number: non-dimensionalisation of Navier-Stokes equation and transition to turbulence. Open questions. Viscous flow between a pair of infinite plates, including plane Couette and Poiseuille flow. Viscous flow through a cylindrical pipe (circular Poiseuille flow). Circular Couette flow. Irrotational flow (streamfunction approach). Basic setup of shallow-water system and derivation, including discussion of how shallow-water-height equation substitutes for mass density and temperature. Gravity waves. Viscosity and Rayleigh drag. Alfven waves and magnetic tension. Poincare and Rossby waves. Basic setup for a plane-parallel shock. Bernoulli’s constant. Rankine-Hugoniot jump conditions. Pre- versus post-shock Mach numbers. Oblique shocks. Basic setup and history of de Laval nozzle. Simplest model of de Laval nozzle. Sophisticated model of de Laval nozzle that allows for shocks to form. Wind tunnel examples. Application to atmospheric escape. Discussion of Ertel’s paper on potential vorticity. Derivation of potential vorticity from momentum equation. Discussion of choice of projection surface for potential vorticity. Kelvin’s circulation theorem. When does potential vorticity conservation break? Application to weather prediction. Boundary layers. Thermal (Benard) instability. Zhukhovsky airfoil. Examples of exam questions, discussion of what kinds of questions to expect.
