
A Course in Fluid Dynamics
Dr. André M. Sonnet
Dipartimento di Matematica,
Università di Pavia,
via Ferrata 1, 27100 Pavia, Italy
Contents
Preliminaries

Tensors and Vectors.

Kinematics.
Balance Equations

Conservation of mass.

Transport Theorems.

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 NAVIERSTOKES equations.
The vorticity equation. Variational characterization of irrotational motions:
KELVIN theorem. Bernoullian theorems. Simple solutions of
NAVIERSTOKES equations. Similarity: REYNOLD's
number. STOKES paradox; OSEEN solution.
Twodimensional motions

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 KUTTAZUKOVSKY theorems;
aerofoils.

Motion of bodies in a fluid. Virtual mass.
Possible Advanced Topics

Stability of fluid motions.

Dynamics of Liquid Crystals.

Viscoelastic Liquids.
Calendar
Classes meet on Tuesday (1213) and Friday (1113) 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
