ATM S 509/OCEAN 512 Geophysical Fluid Dynamics I

Winter 2007
http://www.atmos.washington.edu/2007Q1/509/

MWF 10:30-11:20: Lectures in ATG 310c
Th 1:30-2:20: Lab demonstrations in Oceanography's GFD Lab), OSB 107, led by Peter Rhines
Instructor:
Prof. Chris Bretherton
breth@atmos.washington.edu
ATG 710, x5-7414
Office hours: MW 11:30-12:20,
or by appointment.

  
Teaching Assistant:
Tom Connolly
tompc@u.washington.edu
OSB 343, x3-8543
Office hours TuTh 2:30-3:30


Course description Prerequisites Syllabus Textbook Grading Schedule Homework and Exams Lecture notes Animations

Course Description

Dynamics of rotating stratified fluid flow in the atmosphere/ocean and laboratory analogues. Equations of state, compressibility, Boussinesq approximation. Geostrophic balance, Rossby number. Poincare, Kelvin, Rossby waves, geostrophic adjustment. Ekman layers, spin-up. Continuously stratified dynamics: inertia gravity waves, potential vorticity, quasigeostrophy.

Prerequisites

A course in basic fluid mechanics, such as AMATH 505/ATMS 505/OCEAN 511

Textbook

Gill, A.E., 1982: Atmosphere-Ocean Dynamics. Academic Press [G in syllabus]

Other useful texts:
Cushman-Roisin, B., 1994: Introduction to Geophysical Fluid Dynamics, Prentice-Hall, 320 pp. (recommended; a good basic treatment) [CR in syllabus]
Pedlosky, J., 1979: Geophysical Fluid Dynamics. Springer-Verlag (more mathematically sophisticated and in-depth, esp. for discussions of vorticity, PV, and quasigeostrophic scaling). [P in syllabus]

Syllabus

(updated as term progresses)
Lecture number Date Topic Suggested Reading (G: Gill, P: Pedlosky, CR: Cushman-Roisin)
1-3 Jan 3-8 What is GFD?. Density of air/water. Compressibility and potential density/temperature. Hydrostatic balance in a fluid at rest. Static stability. G1-2,3.1-3.7; CR 1
4-8 Jan 10-22 Scale analysis. The hydrostatic approximation and pressure coordinates. The Boussinesq approximation. Rotating reference frame. Eqns. of motion for stratified, rotating incompressible flow on a sphere. The f and beta plane approximations. Geostrophic and thermal wind balance. G4, 7.6-7.7; P1, 2.6-2.9, 6.1-6.2; CR 2-3
9-10 Jan 24-26 Shallow water equations (SWE) and two-layer approximation. G5.6-5.8, 6.1-6.3, P3.1-3.6
11-17 Jan 29- Feb 12 Rotating linear SWE on an f-plane. Rossby adjustment problem. Potential vorticity. Inertial oscillations, Poincare waves, dispersion and group velocity, Kelvin waves. Flow over a ridge. G7.2, 8.1-8.6, 10.2-10.5 ; P3.7-3.9; CR 6.2-6.3
18-20 Feb 14-21 Rossby waves on a beta plane. Quasigeostrophy. G12.1-3, P3.10-3.19; CR 6.4-5
21-22 Feb 23-26 Ekman layers, Ekman pumping, and Sverdrup transport. G9.6, 9.2, 9.4, 9.12, 11.13, 12.4; P4.1-4.7; 5.1-5.4; CR 5
23-24 Feb 28-Mar 2 Linear internal inertia-gravity waves in a continuously stratified fluid. Critical levels.  Mountain waves. G6.4-6.8, 8.4-8.9
25-27 Mar 5-9 Circulation, vorticity and potential vorticity in a continuously stratified rotating fluid G7.9-11, P2.1-2.5

Grading

Special days

Homework and Exams

Item Due Date Download Solutions
Homework 1 due Fr 19 Jan HW1 Solutions
Homework 2 due Fr 26 Jan HW2 solutions
Homework 3 due Fr 2 Feb HW3 solutions
Take-home midterm due Fr 9 Feb Midterm Solutions
Homework #4 due Fr 16 Feb HW4 solutions
Homework #5 due Fr 23 Feb HW5 solutions
Homework #6 due Fr 2 Mar HW6 solutions
Homework #7 due Fr 9 Mar HW7 solutions
Take-home final due 5 pm Fr 16 Mar Final solutions

Lecture notes

Animations

Linear shallow water equations on an f-plane.

Slab-symmetric LSWE examples (no y-variation). Dots= fluid parcels at mid-height. Colors= v velocity (red = away, blue = toward you).

LSWE in a channel. Perspective plots with free-surface height perturbation color-shaded and arrows on bottom indicating horizontal fluid velocity vector.

TOPEX view of oceanic equatorial Kelvin waves(10 MB) during 1997-2001 using satellite altimetry that sensitively measures the average sea-surface height to within a few cm. The waves are seen as rapid eastward-propagating pulses of changed sea-surface height along the equator; a prominent Kelvin wave is right at the beginning. If you look carefully when a Kelvin wave hits the S American coast, you can often see coastally-trapped Kelvin waves flit poleward in each hemisphere. Slower changes are associated with the evolution of El Nino and midlatitude ocean circulations.

Matlab scripts

Matlab scripts relevant to class material will be posted here:

Name Description

<breth@atmos.washington.edu>