Lectures: 3 sessions / week, 1 hour / session
Prerequisites: 2.25 or an equivalent intermediate level course in Fluid Mechanics or permission of instructor, plus one advanced level engineering mathematics course at the level of 18.085 or 1.131J(2.090J/13.475J) or equivalent.
Advanced treatment of fluid dynamics intrinsic to natural physical phenomena and/or engineering processes. A wide range of topics and mathematical techniques are discussed and may vary from year to year. Modules may be taken by students with different interests.
Sample topics include: Brief review of basic laws of fluid motion. Cartesian tensor convention.Scaling and approximations. Slow flows: Stokes' flow past a particle. Oseen's improvement for a cylinder. Spreading and gravity current on a slope. Selective withdrawal from a stratfied fluid. Boundary layers in high speed flows: Jets. Thermal plumes in pure fluids and in porous media. Similarity method of solution. Transient boundary layers. Buoyancy driven convection in porous media. Dispersion in steady or oscillatory flows. Introduction to hydro-dynamic instability. Linearized analysis of Kelvin-Helmholtz instability. Effects of shear and stratifcation. Orr-Sommerfeld equation for boundary layer instability. Geophysical fluid dynamics of coastal waters. Effects of earth rotation on coastal flows. Wind-induced flows in shallow seas. Coastal upwelling.