Autumn 2006: ATMS 505 / AMATH 505 / OCEAN 511

Introduction to Geophysical Fluid Dynamics

Lectures: MWF 11:30-12:20, Room MEB 103
Lab: Thursday 10:30-11:20, Room MEB 246

Final Exam: In-class Wednesday, Dec 13, 2:30-4:30 PM

Lab on Thursday October 26th in OTB 206

Instructor: Professor Dale Durran
606 ATG, 543-7440, durrand@atmos.washington.edu
Office hours: Monday and Wednesday 2:30-3:30

TA: Sally Warner
343A OSB, 543-8543, sally2@u.washington.edu
Office hours held in 343A OSB : Tues 10:30-11:30, Thurs 2:00-3:00

Textbook: Kundu-Cohen, 2004: Fluid Mechanics,  3rd Ed.  Academic Press.

Overview: 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. 



Reading Assignments
  • Chapter 1 by lab on Thursday, Oct 5th
  • Read Chapter 2 to gain sufficient familiarity with the material to be able to refer back to it as needed when performing mathematical manipulations.
  • Chapter 3, Sections 1-13 by lab on Thursday Oct 12th

Left photo © 2001 Brooks Martner; right photo © 1999 Beverly Shannon

Homework

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) (corrected): Due Wednesday October 11th

Exercise 2 (pdf): (Revised version now posted; delete "viscous" from line 1 of Problem 5 in the old version.) Due Wednesday October 25th

Midterm/Exercise 3 (Prob. 2 slightly revised) (pdf): Work independently. Due Wednesday, November 8th. (Weight in final grade is the same as other homeworks.)

Exercise 4 (pdf) (Prob. 4 deferred until next assignment, additional comments added): Due Wednesday, November 22nd

Exercise 5 (pdf): Due Wednesday, December 6th.

Lab Notes

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. .

Lab 5: Flow over an obstacle: Photograph of clouds showing the top of a bora flow (left to right) down the slopes of Dinaric Alps in Croatia. (From Smith, 1987, Aerial Observations of the Yugoslavian Boral , J. Atmos. Sci., 44, 269-297.)

Lab Photos (courtesy of Bob Koon)

Web Links

Website with all National Committe for Fluid Mechanics films

Course Outline


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

Useful approximations

·        Hydrostatic balance

·        Irrotational and nondivergent flow

·        Heuristic discussion of the Boussinesq approximation; buoyancy

Vorticity dynamics

·        Circulation, Kelvin’s and Bjerknes’ theorems

·        Vorticity equation

·        Vortex lines, Helmholtz theorem

·        Ertel Potential Vorticity

Plane-wave kinematics

·       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)

·        Internal gravity waves

Instabilities; unstable-wave solutions

·        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.