# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 221B: Mathematical Fluid Dynamics

Approved: 2009-03-01, Albert Fannjiang
Units/Lecture:
Winter, alternate years; 4 units; lecture/term paper or discussion
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
I.M. Cohen and P. K. Kundu, "Fluid Mechanics," Chapters 8, 9, 10, 12, (\$90)
Search by ISBN on Amazon: 0123737354
Prerequisites:
MAT 221A or consent of instructor.
Course Description:
Kinematics and dynamics of fluids. The Euler and Navier-Stokes equations. Vorticity dynamics. Irrotational flow. Low Reynolds number flows and the Stokes equations. High Reynolds number flows and boundary layers. Compressible fluids. Shock waves.
Suggested Schedule:
3 Chapter 8 Scaling, similarity, Buckingham's Pi theorem
2 9.1 - 9.6 Laminar flows between plates, in a pipe, between concentric cylinders
2 9.7 - 9.10 Exactly solvable unsteady laminar flows
2 9.11 - 9.13 Stokes' and Oseen's solutions
1 10.1 - 10.3 Boundary layer approximations
1 10.4 Closed form solution
2 10.5 Blasius solution, Falkner-Skan solution
1 10.6 von Karman momentum integral
2 10.7 - 10.8 Flow separation
1 10.9 Flow past a cylinder, von Karman vortex street
1 10.10 - 10.11 Flow past a sphere
1 10.12 2-d jets
1 10.17 Laminar shear layer
2 12.3 The Benard problem
1 12.5 Taylor instability
1 12.6 Kelvin-Helmholtz instability
1 12.7 Taylor-Goldstein equation, Richardson number criterion
1 12.7 Howard's semicircle theorem
1 12.8 Squire's theorem, Orr-Sommerfeld equation
1 12.9 Rayleigh's inflection point criterion, Ejortoft's theorem
1 12.10 Boundary layer instability