Math 228: Mathematical Fluid Dynamics (Spring 2012)

This course is designed to give an overview of fluid dynamics from a mathematical viewpoint, and to introduce students to areas of active research in fluid dynamics. This course is aimed at first year graduate students in mathematics, physics, and engineering.

Topics to be covered:

Derivation of the governing equations: Euler and Navier-Stokes
Flow kinematics, Conservation laws and Vorticity
Inviscid, irrotational flows: potential flow and complex variables
Classical laminar flows
Boundary Layers and Asymptotic Models in Fluid Dynamics
Water waves
Flow Instabilities

Prerequisites

Some background in solving ordinary and partial differential equations, basic physics/mechanics, multivariable calculus.

Schedule

Wed/Fri, 1:15-2:30pm, Room 119 Physics Building

First class meeting: "Classes meeting in a Wednesday/Friday meeting pattern begin January 13" -- see Academic Calendar

Instructor

Thomas Witelski, Professor, Dept of Math

Office hours

(Tentative) Mondays 1:00-3:00 pm, or by email request for an appointment for other times.

Textbook

Elementary Fluid Dynamics by D. J. Acheson (Oxford University), Oxford University Press

Problem sets

Course materials and web links

Course outline
Review sheets
- Vector algebra summary
- Vector calculus summary
- ODEs and complex algebra summary
- Cartesian tensors and index notation
- Polar coordinates
- Contour Integrals and residues summary
Lecture notes
- Lecture 1: intro to flow kinematics
- Lecture 2: local expansion of the velocity field
- Lecture 5: the equations of fluid dynamics
- Lecture 5: boundary conditions
- Lecture 8: review of complex variables
- Lecture 11: III flows around circular cylinders
- Lecture 16: Time-dependent uni-directional viscous flows
- Lecture 17: Intro to asymptotic problems in fluid dynamics
- Lecture 18: Intro to Stokes flows
- Lecture 19: Stokes' paradox and perturbation methods/problems
- Lecture 25: Dispersive water waves
- Lecture 26: Interface stability problems
NCFMF Fluid Mechanics Film Series at MIT
Computer access: Duke OIT VPN (set Dept to "Library Resources Only")

Reference books

Theoretical hydrodynamics by L.M. Milne-Thomson
An introduction to theorertical fluid mechanics by S. Childress
Fluid Mechanics by Kundu and Cohen
Fundamental Mechanics of Fluids by I. G. Currie
A mathematical introduction to fluid mechanics by Chorin and Marsden
Fluid dynamics for physicists by T. E. Faber
Physical fluid dynamics by D. J. Tritton