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:

Lectures Sections Topics/Comments
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

Additional Notes:

COMMENT: I taught 221AB from this book in 2007-2008 and appreciated the clarity, readability and variety of interesting topics covered in the book. Cohen & Kundu also has a lot more material than one can cover in a two-quarter course. It is, however, not written in the style of a typical "mathematical fluids" book. For the latter, one can consult, e.g., the well written Mathematical Theory of Incompressible Nonviscous Fluids by Marchioro and Pulvirenti. Such books are often more focused but limited in scope.