Math 575: Mathematical Fluid Dynamics (Spring 2019) [5946]
This course is designed to give an overview of fluid dynamics and the
mathematical techniques used to study some of the many sub-classes of
fluids problems.
This course is aimed at first year graduate
students in mathematics, physics, and engineering.
- Derivation of the governing equations: Euler and Navier-Stokes
equations
- Flow kinematics, Conservation laws and Vorticity
- Inviscid, irrotational flows: potential flow and complex variables
- Classical laminar flows
- Low Reynolds number flows: Stokes and Lubrication equations
- Dimensional scaling, Asymptotic Models, and Boundary
Layers in Fluid Dynamics
- Water waves
- Flow Instabilities
Prerequisites
Background in solving ordinary and partial differential equations,
basic physics/mechanics, multivariable calculus.
Math 575-01 (5946) Mathematical Fluid Dynamics
Tu/Th, 1:25-2:40pm, Room 259 Physics Building
- First class meeting: Thurs, Jan 10 --
see Academic Calendar
- Lectures end: Tues, April 23
Instructor
Thomas Witelski, Dept of Math
Office hours
Schedule to be announced,
or by email request for an appointment for other times.
Textbook
Problem sets
Course materials and web links
Reference books
- Elementary Fluid Dynamics by D. J. Acheson
- 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