AE 201c: Hydrodynamic Stability, Dr. Pullin
Content:  Linear stability analysis and normal mode analysis, Kelvin-Helmholtz instability, Rayleigh-Taylor instability, shear instability, break-up of a liquid jet, thermal instability, Boussinesq approximation, Richtmyer-Meshkov instability, centrifugal instabilities, inviscid instabilities, axisymmetric inviscid disturbances, two-dimensional disturbances, Couette flow, Dean's problem, Gortler's problem, parallel shear flows, squire's theorem, inflection point theorem, Fjortott's theorem, Orr-Sommerfeld equation, plane Poiseuille flow, Blasius boundary layer, transient growth,
Books: Class notes;
Drazin, PG and Reid, WH, "Hydrodynamic Stability", Cambridge University Press 2003

AE 201b: Advanced Fluid Mechanics, Compressible Flows, Dr. Pullin
Content: Compressible flow, hodograph method; shock waves, Navier-Stokes shock structure, shock dynamics, shock-jump relations, shock reflection and Mach reflection, Guderley implosion problem, approximate methods for shock dynamics, geometrical shock dynamics, strong shocks, wave propagation on shocks, shock stability, the Riemann problems; molecular gas dynamics, kinetic theory, velocity distribution functions, Maxwellian distribution, molecular fluxes,
Books: Class notes

 

AE 201a: Advanced Fluid Mechanics, Incompressible Flows, Dr. Pullin
Content:  Continuum approach and description, kinetic theory of gases, Lagrangian and Eulerian specification of motion, Newtonian fluids, viscosity in gases, Navier-Stokes and Euler equations and boundary conditions, well-posedness of equations, incompressible and Stokes limits, energy equations, dissipation of kinetic energy in incompressible flows; low Mach number expansion of compressible Euler; vorticity, energy associated with vorticity, vorticity dynamics, Helmholtz vorticity laws, vorticity equations, point vortex dynamics, Hill's spherical vortex, viscous vorticity equations; exact solutions of Navier-Stokes equations, Couette and Poiseuille flows, Rayleigh flows, circular Couette flow, Burger's vortex, flows in channels with fluctuating pressure gradients, stagnation point flows, flow with rotation, flow past bodies; potential flow, Stoke's streamfunction, free streamline theory; diffusion and mixing,
Books: Class Notes