A Course in Fluid Dynamics
Dr. André M. Sonnet
Dipartimento di Matematica,
Università di Pavia,
via Ferrata 1, 27100 Pavia, Italy
Tensors and Vectors.
Conservation of mass.
Stress Tensor. Contact and body forces: CAUCHY hypothesis;
CAUCHY theorem. Consequences: theorem of expended power.
Constitutive Equations. General requirements: Frame indifference, causality,
locality. Constitutive assumptions for Eulerian and Newtonian fluids.
EULER and NAVIER-STOKES equations.
The vorticity equation. Variational characterization of irrotational motions:
KELVIN theorem. Bernoullian theorems. Simple solutions of
NAVIER-STOKES equations. Similarity: REYNOLD's
number. STOKES paradox; OSEEN solution.
Steady Motions. General concepts: stream function, stagnation points.
Velocity potential; complex potential and complex velocity: examples.
Boundary layers: PRANDTL equations.
Forces on obstacles. D'ALEMBERT paradox.
The BLASIUS and KUTTA-ZUKOVSKY theorems;
Motion of bodies in a fluid. Virtual mass.
Possible Advanced Topics
Stability of fluid motions.
Dynamics of Liquid Crystals.
Classes meet on Tuesday (12-13) and Friday (11-13) in
Aula Berzolari in the Department of Mathematics.
Inaugural Lecture on 1 December 2000 at 11 c.t. in Sala Riunioni, floor C, Department of Mathematics