Autumn 2008: ATMS 505 / AMATH 505 / OCEAN 511
Final Exam: In-class Wednesday, Dec 10, 2:30-4:30 PM
Professor Dale Durran
408 ATG, 543-7440, firstname.lastname@example.org
Office hours: Monday and Wednesday 2:30-3:30
Special office hours Monday Dec 8, 1:30-3:00 PM.
TA: Lucas Harris
426 ATG, 543-4952, email@example.com
Office hours in ATG 420: Tues 10:30-11:30
Textbook: Kundu-Cohen, 2004: Fluid Mechanics, 4th Ed. Academic Press.
The purpose of the course is to obtain a thorough understanding of the
basic mathematical relations that describe atmospheric and oceanic
motions. We will consider both the fundamental governing
equations applicable to almost all geophysical motions and simplifed
models describing elementary stable and unstable circulations.
Left photo © 2001 Brooks Martner; right photo © 1999 Beverly Shannon
Policy for late homework for homeworks due on Wednesday: papers submitted after class, but before the end of Wednesday -10%; papers submitted Thursday -25%, papers submitted Friday -35%. No late homework will be accepted after Friday.
Exercise 1 (pdf): Due Wednesday October 8th
Exercise 2 (pdf): (Notational clarification added to problem 2) Due Wednesday October 22nd
Midterm/Exercise 3 (pdf): (Prob 4 is now reworded.) Work independently. Due Wednesday, November 5th. (Weight in final grade is the same as other homeworks.)
Exercise 4 (pdf): Due Wednesday, November 19th
Exercise 5 (pdf): (Minor editing added to Prob 4.) Due Wednesday, December 3rd
Lab 1: Weather Ball: example of variations in atmospheric pressure (green curve) and temperature (red curve) at Seatax Airport betweeen 15 UTC (8 AM PDT) on September 27 to 15 UTC on September 29, 2006. Note that the water in the outflow tube of the weather ball will rise roughly one cm due to a 1.2 K increase in the temperature of the air inside the sphere or a 1 hPA (1 mb) drop in the atmospheric pressure. Writeup.
Lab 2: Cartesian Diver: Writeup
Lab 4: Vorticity Kinematics: Writeup.
Lab 5: Bernoulli's Principle: Writeup.
Lab 7: Vorticity Dynamics: Writeup.
Lab 8: Surface Waves: Writeup.
Lab 10: Multi-layer fluids Writeup.
· Classical thermodynamics
· Static stability
Physical conservation laws applied to a continuum
· Conservation of momentum (Newton’s 2nd Law)
· Conservation of mass
· Conservation of energy (First Law of thermodynamics)
· Equations of state
· Lagrangian and Eulerian coordinates
· Hydrostatic balance
· Irrotational and nondivergent flow
· Heuristic discussion of the Boussinesq approximation; buoyancy
· Circulation, Kelvin’s and Bjerknes’ theorems
· Vorticity equation
· Vortex lines, Helmholtz theorem
· Ertel Potential Vorticity
· Wave phase, wave vector, wavenumber, and wavelength
· Frequency, period, and phase speed
· Imaginary phase (growth in space and/or time)
· Group velocity
Linearizing nonlinear equations; neutral-wave solutions
· Surface gravity waves (water waves)
· Kelvin-Helmholtz instability
Grading: 75% of the grade will be based on five homework assignments; the remaining 25% on the final. One homework assignment will be a take-home midterm (worth 15% of the total grade, just like all the other homeworks). The take-home midterm must be done independently. You may work with other students on the other four homeworks.