Autumn 2008: ATMS 505 / AMATH 505 / OCEAN 511

**Introduction to
Geophysical Fluid Dynamics
**Lectures: MWF 11:30-12:20, Room ATG 610

Lab: Thursday 10:30-11:20, Room OTB 206

Final Exam: In-class Wednesday, Dec 10, 2:30-4:30 PM

*Instructor:*
Professor Dale Durran

408 ATG, 543-7440, durrand@atmos.washington.edu

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, lharris@atmos.washington.edu

Office hours * in ATG 420*: Tues 10:30-11:30

*Textbook:* Kundu-Cohen, 2004: *Fluid Mechanics, 4th 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.

- Chapter 1 by lab on Thursday, Oct 2nd
- 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 9th
- Chapter 4, Sections 1-7,10-11, 13-16 by lab on Thursday Oct 16th
- Chapter 4, Section 17; Chapter 5, Sections 1-3 by lab on Thursday Oct 23th
- Chapter 5, Sections 4-6, 8-9 by lab on Thursday Oct 30th.
- Chapter 7, Sections 1-6, and the notes on plane waves (download pdf), by lab on Thursday November 6th.
- Chapter 7, Sections 8-11 by lab on Thursday November 12th
- Chapter 7, Sections 18-21 by Wednesday November 19th
*Skim*Chapter 7, Sections 13-14.*Read*Chapter 12, Sections 1,2,6 by Lab on Thursday November 26th- Aaron Donohoe makes KH billows in Cambridge
- Animation of KH instability

Kelvin-Helmholtz billows in the atmosphere

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): 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 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. *Writeup.*

*Lab 2: Cartesian Diver: Writeup*

*Lab 3: U-tubes: Writep. Notes on Pressure.*

*Lab 4: Vorticity Kinematics: Writeup.*

*Lab 5: Bernoulli's Principle: Writeup.*

*Lab 6: Open Channel Flow: Writeup. For another interpretation of open channel flow see Section 3 of This.*

*Lab 7: Vorticity Dynamics: Writeup.*

*Lab 8: Surface Waves: Writeup.*

*Lab 9: Stirring and Mixing: Writeup.*

*Lab 10: Multi-layer fluids Writeup.*

- Eulerian and Lagrangian Description of Fluid Flow (John Lumley); The National Committee for Fluid Mechanics Films
- Vorticity Part I (Ascher Shapiro) The National Committee for Fluid Mechanics Films
- Vorticity Part 2 (Ascher Shapiro) The National Committee for Fluid Mechanics Films
- Pressure Fields and Fluid Acceleration (Ascher Shapiro) The National Committee for Fluid Mechanics Films.

*Course Outline
*

**
**

· Statics

· Classical thermodynamics

· Static stability

Physical conservation laws applied to a continuum

·
Conservation
of momentum (Newton’s 2^{nd }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

· 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.