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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 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.
Two-dimensional 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 KUTTA-ZUKOVSKY 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 (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