
A Course in Fluid Dynamics
Prof. Epifanio G. Virga
Dr. André M. Sonnet
Dr. Riccardo Rosso
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
of Eulerian fluids

Steady Motions. General concepts: stream function, stagnation points. Velocity potential; complex potential and complex velocity: examples. Rigid boundaries: the circle theorem; the rôle of conformal transformations: ZUKOVSKY's transform. Sources and sinks: the image method.

Forces on obstacles. D'ALEMBERT paradox. The BLASIUSKUTTAZUKOVSKY theorem; aerofoils.

Motion of bodies in a fluid. Virtual mass.
Vortex Motions

Different types of vortices. Circular vortex; vortex filaments: centroid of a vortex filament; vortex pairs; vortex sheets; vortex patches; VON KÁRMÁN street. Line and ring vortices. Conserved quantity in vortex motions; helicity. HILL and KIRCHHOFF vortices.

Stability of vortices. KELVINHELMHOLTZ instability.

Vorticity and viscosity. Diffusion of vorticity in a Newtonian fluid. Effects of viscosity on vortex motions.
Advanced Topics

Stability of fluid motions.

Dynamics of liquid Crystals.

Dynamics of deformable bodies in a fluid.
Bibliography

K. R. Rajagopal, C. A. Truesdell An Introduction to the Mechanics of Fluids, Birkäuser (1999).
C. A. Truesdell A First Course in Rational Continuum Mechanics, Vol.1, second edition, Academic Press (1991).
P. G. Saffmann Vortex Dynamics, Cambridge University Press (1992).
Calendar
Classes meet on Tuesday (46 p.m.) and (only in October) Thursday (35 p.m.) in
Sala Conferenze at floor C in the Department of Mathematics.
