Syllabus
1. Some examples of analytical solutions to the Navier--Stokes equations. Viscometric flows.
2. Some examples of analytical solutions in the linearized theory of elasticity. Elastic potentials, stress concentration factors. Waves in elastic materials.
3. Stability of fluid flows. Energy method, linearized stability theory and its limits, Orr-Sommerfeld equation, self sustaining processes.
4. Oberbeck-Boussinesq aproximation, Rayleigh-Bénard problem. Finite amplitude disturbances. Lorentz equations.
5. Flow past bodies, drag and lift. Prandtl boundary layer theory.
Annotation
The aim of the subject is to introduce some classical problems in continuum mechanics, and discuss their physical background and related mathematical techniques that have been developed in order to solve these problems. The spectrum of the problems studied during the lecture is deliberately very broad and the lecture should provide a summary of some major achievements in the field.