|
Syllubus
|
This Web Site is a basic resource for APPH 4200. Copies of my lecture notes will be available for download in Adobe PDF formats.
A preliminary lecture plan is llisted below. I anticipate changes as we move along. Some topics may require more lecture time, and some will require less. Depending on your interests and comments, we may change some of the topics in the last third of the course.
| Lecture Dates |
Topics |
| Sept 8, 10 |
Introduction to Fluids.
Mathematical Preliminaries: Cartesian tensors.
Chapters 1 and 2
Lecture 1 Notes
See discussion about lift generated by fluid flow around a rotating cylinder at NASA's Glenn Research Center.
Lecture 2a Notes
Lecture 2b Notes
Download useful vector identities (and plasma and hydro info)
Naval Research Lab's Plasma Formulary.
|
| Sept 15, 17 |
Mathematical Preliminaries: Cartesian tensors.
Chapter 2
Lecture 3 Notes
Basic kinematics: Lagrangian vs. Eulerian,
Streamlines & trajectories, total derivative,
Mass continuity.
Chapter 3
Lecture 4 Notes
|
| Sept 22, 24 |
Derivation of Navier-Stokes equation.
Balance of forces. Bernoulli's Equation.
Stress and strain tensors, definition of a Newtonian fluid.
Effects of a rotating reference frame.
Chapter 4
Lecture 5 Notes
Lecture 6 Notes
Read about the Clay Mathematics Institute's Navier-Stokes $1,000,000 challenge at this link. |
Sept 29
Oct
1 |
Fluids in the news: Circulation in Monterey Bay (NY Times, Sept 28, 2009). See gorgeous pictures of trapped and open path lines in the Monterey Bay.
Using the conservation equations…
Chapter 4
Lecture 7 Notes
Vorticity
Chapter 5
Lecture 8 Notes
Fluid Video Gallery from Melbourne, AU, with colloiding vortex rings.
|
| Oct 6, 8 |
"Anatomy of a Bathtub Vortex," by A. Andersen and co-authors, Physical Review Letters, Vol. 91, p. 104502 (2003).
More Chapter 5
Lecture 9 Notes
Irrotational flow.
Potential flow theory.
Potential flow around obstacles: lift and drag.
Chapter 6
Lecture 10 Notes
Link to "complex analysis" at Wolfram's MathWorld.
Mathworld's page on Cauchy-Riemann Equations.
Nice biography of Paul Richard Heinrich Blasius (1883-1970). |
Oct 13, 15 |
Lecture 11 Notes (Ch. 6)
Numerical example prepared using Mathematica. Mathematica is available in all Columbia University computer labs, and a student license is available.
Mathematica notebook and print-out in pdf.
Dimensional analysis, similarity.
Reynolds number.
Laminar boundary-layer theory, drag on thin flat plate.
Chapter 9
Lecture 12 Notes (Ch. 8 & 9) |
| Oct 20, 22, 27 |
More Chapter 9...
Lecture 13 Notes (Ch. 9)
Lecture 14 Notes (More Ch. 9)
Lecture 15 Notes (Midterm Review)
Vortex Sheading Video (a great student project, entertaining to watch) |
Thursday
Oct 29 |
MIDTERM
(Appendecies and Equations attached to exam: here.)
Results are summarized here. |
| Nov 3, 5 |
Election Break (No class: APS Division of Plasma Physics Meeting) |
| Nov 10, 12 |
Waves.
Linear surface gravity waves. Continuously stratified flow.
Shallow and deep water equations.
Lecture 16 Notes (Ch. 7, Surface Gravity Waves)
Lecture 17 Notes (Ch. 7, Internal Gravity Waves)
Lecture 18 Notes (Ch. 7, Capillary Waves & Sound) |
| Nov 17, 19 |
Linear Instability; Benard Thermal Instability; Kelvin-Helmholtz problem:
stability of a sheared flow with stable density stratification.
Chapter 12
Lecture 19 Notes
Mathematica notebook and print-out in pdf.
Lecture 20 Notes
"Transport of solar wind into Earth's magnetosphere through rolled-up Kelvin-Helmholtz vortices", Hasegawa, et al., Nature, 430, 755 (2004).
Lecture 21 Notes (Ch. 12, continued)
(Lorenz Model Mathematica Notebook and PDF file.) |
| Nov 24 |
Rotating and parallel shear flows.
Introduction to turbulence
Chapter 14
Lecture 21 Notes (Ch. 14)
Lorenz Model at Wikipedia Site.
Movie of Turbulent Fluid Mixing from Prof. Thomas Peacock at MIT. |
| Nov 26 |
Thanksgiving Holiday |
| Dec 1, 3 |
Geostrophic and quasi-geostrophic flow.
Chapter 13
Lecture 22 Notes
Lecture 23 Notes
UNISYS Weather site and atmospheric vorticity and flow maps.
Biography of Carl-Gustaf Rossby at American Meteorological Society.
Time magazine's cover story about Rossby and weather forecasting.
Biography of Jule Charney at AGU.
Rossby waves in oceans, Chelton and Schlax,Science, 1996.
Rossby waves on the sun, Kuhn, et al., Nature, 2000.
Biography of Jack Bjerknes. |
| Dec 8, 10 |
T.B.D.
Review (and make-up class)
Lecture-Review Notes |
Dec 22
|
FINAL EXAM
Tuesday, 12/22/2009
1:10pm - 4:00pm (MUDD T.B.D.) |
|