MATH 386 Fluid Dynamics

The ideal fluid. Irrotational flow. The vorticity equation. Steady flow past a wing. The equations of viscous flow. The diffusion of vorticity. Flow with circular stream lines. The convection and diffusion of vorticity. Waves. Surface waves. Dispersion, group velocity. Surface tension effects. Effects of finite depth. Sound waves. Classical Aerofoil Theory. Velocity potential and stream function. Method of images. Milne-Thompson’s Circle theorem. Complex potential. Conformal mapping. Blasius’ theorem. The Kutta- Juokowsli lift theorem. D’Alembert’s paradox. Vortex motion. Kelvin’s circulation theorem. The Helmholtz vortex theorems. Navier Stokes Equations. Very viscous flow.