2006 Spring MATH 228-01
Bulletin Course Description Properties and solutions of the Euler and Navier-Stokes equations, including particle trajectories, vorticity, conserved quantities, shear, deformation and rotation in two and three dimensions, the Biot-Savart law, and singular integrals. Additional topics determined by the instructor. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title MATHEMATICAL FLUID DYNAM Department MATH Course Number 2006 Spring 228 Section Number 01 Primary Instructor Oron,Alex Permission required? N
Prerequisites
Math 114, Math 133 or equivalents -- some background in analytical methods for solving basic partial differential equations is needed.
Synopsis of course content
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:
1) Derivation of the governing equations: Euler and Navier-Stokes
2) Flow kinematics, Conservation laws and Vorticity
3) Irrotational flow: potential flow and complex variables
4) Water waves and Geophysical Fluid Dynamics
5) Classical laminar flows
6) Boundary Layers and Asymptotic Models in Fluid Dynamics
7) Flow Instabilities
Textbooks
Fluid Mechanics by P.K. Kundu and I. M. Cohen, 3rd edition, 2004
Assignments
There will be regularly assigned weekly or bi-weekly problem sets.
Exams
No exams.
Grade to be based on
Course grade will be based on the problem sets and a possible
end-of-term project.
