Math 654: Introduction to Fluid Dynamics                Winter 2014
Instructor: Silas Alben, 5836 East Hall, tel. 734-647-5518,
email: alben at umich.edu (usually the best way to contact me).


Time and Location:  TuTh 2:30 - 4, 3088 East Hall.
Office hours: Tues. and Wed. 10-11 (subject to change) or by appointment.


HW 1, due Jan. 28

Reading for Jan. 9, Jan. 14, Jan. 16: Acheson, Chapter 1.
    A few optional films from http://web.mit.edu/hml/ncfmf.html:
        Deformation of Continuous Media (see "film notes" also)
        Eulerian Lagrangian Description (see "film notes" also)
        Flow Visualization (see "film notes" also)

Reading for Jan. 21, Jan. 23: Acheson, Chapter 2.

Reading for Jan. 28, Jan. 30: Acheson, 3.1-3.8.
    An optional film from http://web.mit.edu/hml/ncfmf.html:
        Waves in Fluids (see "film notes" also)

Reading for Feb. 4, Feb. 6: Acheson, 3.9-3.11.

Reading for Feb. 11, Feb. 13: Acheson, 4.1-4.8.

Reading for Feb. 18, Feb. 20: Acheson 4.9-4.13.

Reading for Feb. 25--Mar. 13: Acheson Chap. 5
    Optional films from http://web.mit.edu/hml/ncfmf.html:
        Vorticity, Part 1 and Part 2 (see "film notes" also)

Reading for Mar. 18--20: Acheson Chap. 6

Reading for Mar. 25--27, Apr. 1--3: Acheson Chap. 7
    Optional film from http://web.mit.edu/hml/ncfmf.html:
        Low Reynolds Number Flow (see "film notes" also)


HW 2, due Feb. 27:
    Acheson 3.1, 3.6, 3.10, 3.13, 3.18, 3.20, 4.4, 4.5, 4.8, 4.10

HW 3, due Apr. 3:
    Acheson 5.6, 5.10, 5.16, 5.25, 6.6, 6.8, 6.12

HW 4, due Mon., Apr. 28 at noon:
    Acheson 7.3, 7.9, 8.2, 8.4, 9.1

Reading for Apr. 3, 8, 10: Acheson Chap. 8.

Relevant films from http://web.mit.edu/hml/ncfmf.html:
Fundamentals-Boundary Layers
Secondary Flow

Reading for Apr. 15, 17, 22: Acheson Chap. 9.
 
Relevant films from http://web.mit.edu/hml/ncfmf.html:
Flow Instabilities
Turbulence



Course Description:
The course is a broad introduction to fluid dynamics. We'll use
classical applied mathematical tools to gain physical insight into
fluid phenomena. No knowledge of fluid mechanics is assumed,
but some upper-level undergraduate mathematics is
(see pre-reqs below).

Topics: Continua and conservation laws. Inviscid flow.
Irrotational flow. Vorticity. Complex variable methods. Airfoil
theory and conformal transformations. Viscosity and the Reynolds
number. The limit of zero Reynolds number. Boundary layers.
Flow instabilities.

Pre-requisites: Vector calculus. Complex analysis and differential
equations at a senior undergraduate level (Math 450).
Elementary physics (mechanics). Please contact me if you are unsure
about the pre-requisites.

Required text:
Elementary Fluid Dynamics by D. J. Acheson, Oxford University Press, 1990.

Not required but recommended:
The "Multimedia Fluid Mechanics" DVD, 2nd edition,
Publication Date: February 2, 2011 | ISBN-10: 0521721695 |
ISBN-13: 978-0521721691.

Fluid dynamics is a very visual subject. The DVD contains
many films and animations which are quite instructive.
These will be discussed occasionally in class.

A link to some classic fluid dynamics films from MIT
(some clips of which are on the DVD):
http://web.mit.edu/hml/ncfmf.html

Some other useful texts:
“An Introduction to Fluid Dynamics”, G.K. Batchelor, Cambridge University Press
“A Mathematical Introduction to Fluid Mechanics”, A.J. Chorin & J.E. Marsden, Springer
“Fluid Mechanics”, L.D. Landau & E.M. Lifshitz, Pergamon
"Fluid Mechanics", P. K. Kundu & I. M. Cohen, Elsevier.

Grading: The grade will be based on homework assignments given
every 2-3 weeks as well as class attendance and participation.

A link to Applied Mathematics Fellowships, Internships, Workshops from Robert Krasny:
http://www.math.lsa.umich.edu/~krasny/fellowships_etc.html