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 2, 4 
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 9, 11 
Mathematical Preliminaries: Cartesian tensors.
Chapter 2
Lecture 3 Notes
Fluids in the news (922014): Soliton Turbulence seen for the first time on North Carolina’s Coast. See "Soliton Turbulence in Shallow Water Ocean Surface Waves," PRL, 113, 108501. By Andre Costa, a PhD student at AixMarseille Université, France.
Basic kinematics: Lagrangian vs. Eulerian,
Streamlines & trajectories, total derivative,
Mass continuity.
Chapter 3
Lecture 4 Notes 
Sept 16, 18 
Derivation of NavierStokes 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
Excellent video about Eulerian and Lagrangian Descriptions of Fluids (by Prof. John Lumley, Penn State, 1962). Part 2 is located here. The mathematics is very well explained in Part 2. Finally, Part 3 illustrates a more general vector field and the acceleration of a material element of a fluid.
Read about the Clay Mathematics Institute's NavierStokes $1,000,000 challenge at this link. 
Sept 23, 25 
Fluids in the news:
Prof. Michael Shats and colleagues at the Australian National University show how mean surface flows can be generated through nonlinear effects of surface water waves. At low amplitudes, the mean surface flow is away from the wave generator. But at higher amplitudes, the mean surface flow reverses creating a "water tractor beam". Very beautiful demonstration of nonlinear wave effects in fluids. See article in NaturePhysics, entitled "Generation and reversal of surface flows by propagating waves," v.10, p.658 (Sept 2014).
Using the conservation equations…
Chapter 4
Lecture 7 Notes 
Sept 30, Oct 2 
Vorticity
Chapter 5
Lecture 8 Notes
Fluid Video Gallery from Melbourne, AU, with colliding vortex rings.
See wonderful work by UCSD Pure Electron Plasma Group, including "Vortex crystals from 2D Euler flow: Experiment and simulation", Phys. Fluids, 11(4) 905 (April 1999) and an early news article in Science highlighting both Columbia and the UCSD plasma research.
"Anatomy of a Bathtub Vortex," by A. Andersen and coauthors, Physical Review Letters, Vol. 91, p. 104502 (2003).
More Chapter 5
Lecture 9 Notes
Excellent Vorticity videos from the 1960's Fluid Mechanics Films series. See Vorticity Part 1 and Vorticity Part 2. 
Oct 7, 9 
Simple calculations of 2D motion of line vortices. Mathematica notebook is here Line Vorticies.nb. A video is here ring_vortex.mp4
Potential flow theory.
Irrotational flow.
Potential flow around obstacles: lift and drag.
Chapter 6
Lecture 10 Notes
Link to "complex analysis" at Wolfram's MathWorld.
Mathworld's page on CauchyRiemann Equations.
Nice biography of Paul Richard Heinrich Blasius (18831970).
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 printout in pdf. 
Oct 14, 16 
Dimensional analysis, similarity. Good overview: "Dynamic similarity, the dimensionless science," by Bolster, Hershberger, and Donnelly, Physics Today, Sept, 2011.
Reynolds number.
Laminar boundarylayer theory, drag on thin flat plate.
Chapter 9
Lecture 12 Notes (Ch. 8 & 9)
Lecture 13 Notes (Ch. 9)
Lecture 15 Notes (Midterm Review) 
Tuesday
Oct 21 
MIDTERM
(Appendecies and Equations attached to exam: here.)
Results are summarized here. 
Oct 23 
More Chapter 9...
Lecture 14 Notes (More Ch. 9) Waves
Vortex Sheading Video (a great student project, entertaining to watch) 
Oct 28, 30 
APS Division of Plasma Physics Meeting (New Orleans). Classes cancelled. 
Nov 4 
Election Day Break 
Nov 6 
More waves....
Lecture 16 Notes (Ch. 7, Surface Gravity Waves)
Lecture 17 Notes (Ch. 7, Internal Gravity Waves)
Outstanding Physical Oceanography Lab Demos from Univ Rhode Island
Linear surface gravity waves. Continuously stratified flow.
Shallow and deep water equations. 
Nov 11, 13 
Lecture 18 Notes (Ch. 7, Capillary Waves & Sound)
Lecture 18 (more) Notes (Tides and Stellar Clouds)
Linear Instability; Benard Thermal Instability; KelvinHelmholtz problem:
stability of a sheared flow with stable density stratification.
Chapter 12
Lecture 19 Notes
Mathematica notebook and printout in pdf. 
Nov 18, 20, 25 
Lecture 20 Notes Rotating and parallel shear flows (Chapter 12)
"Transport of solar wind into Earth's magnetosphere through rolledup KelvinHelmholtz vortices", Hasegawa, et al., Nature, 430, 755 (2004).
Three relevant articles reviewing viscous dynamics:
Chapter 10: Ludwig Prandtl and viscous boundary layer
Lecture 22 Notes (Ch. 10)
(Mathematica Notebook and PDF file of numerical solution to boundary layer.)
Nice biographies of Ludwig Prandtl (18751953) and also of his graduate student, Paul Richard Heinrich Blasius (18831970). 
Nov 27 
Thanksgiving Holiday 
Dec 2, 4 
Chapter 13: Introduction to turbulence
Lecture 21 Notes
(Lorenz Model Mathematica Notebook and PDF file.)
Lorenz Model at Wikipedia Site.
Movie of Turbulent Fluid Mixing from Prof. Thomas Peacock at MIT.
Chapter 14 Geostrophic and quasigeostrophic flow.
Lecture 23 Notes
UNISYS Weather site and atmospheric vorticity and flow maps.
Biography of CarlGustaf Rossby at American Meteorological Society.
Time magazine's cover story about Rossby and weather forecasting.
Biography of Jule Charney at AGU.
Good review of Rossby waves by Robert Dickinson (Annual Review of Fluid Mechanics, vol 10, 1978)
Rossby waves in oceans, Chelton and Schlax,Science, 1996.
Rossby waves on the sun, Kuhn, et al., Nature, 2000.
Biography of Jack Bjerknes. 
Dec 9 
Lecture 24 Notes Review for final exam. 
T.B.D.

FINAL EXAM 
