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Geophysical Fluid Dynamics I
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ATM S 509A & OCEAN 512A
Winter Term 2006, 4 credits (SLN1591 & 6929)
Description
This class is intended for first year graduate students in Atmospheric Science and Physical Oceanography. It covers the basic physics of large-scale fluid flow on the Earth, focusing on how stratification and rotation affect important fluid mechanical phenomena. Lectures will be given on the three regular class days. We will also arrange another 1 hour meeting during the week for informal problem and reading discussions, and several lab activities.
Catalog 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. Continuously stratified dynamics: Inertia-gravity waves, potential vorticity, quasigeostrophy. Prerequisite: ATM S/AMATH 505/OCEAN 511.
Grading
- Homework (60%)
- Midterm Exam (15%) Take-home, open book and notes (handed out 2/3, due 2/10).
- Final Exam (25%) Take-home, open book and notes (handed out 3/8, due 3/15 Noon at Yi's office).
Textbooks
- Required: Gill, A. E. (1982) Atmosphere-Ocean Dynamics. Academic Press, 662 pp. This should already be available at the UW bookstore in the textbook section.
- Supplementary: Kundu, P. K., and I. M. Cohen (2002) Fluid Mechanics. Second edition (any edition is OK), Academic Press, 730 pp. You absolutely should own a copy of this. [KC in the Syllabus]
Syllabus
1. Planetary Fluids at Rest
- Wed 1/4 What is GFD? Scales and Questions
- Fri 1/6 Pressure: hydrostatic balance at rest, molecular considerations, and linking gradients to acceleration
- Mon 1/9 Linking gradients to acceleration, Air and Water on Earth: compressibility, thermodynamics, ideal gas, equations of state
- [H1 handed out, due 1/13]
- Wed 1/11 Potential density and potential temperature, the Buoyancy frequency
2. Planetary Fluids in Motion
- Fri 1/13 Review of the equations of motion and mass conservation
- Fri 1/13 Lab: Two layers fluid without rotation
- Mon 1/16 HOLIDAY
- Wed 1/18 Momentum in a rotating frame of reference, and the geopotential
- Fri 1/20 Scale analysis, and the hydrostatic approximation
- [H2 handed out, due 1/27]
- Fri 1/20 Boussinesq approximation
- Mon 1/23 Equations of motion: stratified, rotating, incompressible, on a sphere
- Wed 1/25 The f-plane and Beta-plane, Rossby Number, geostrophic balance, thermal wind
3. Shallow water approximation (homogeneous flow)
- Fri 1/27 Derivation of the Shallow Water Equations (SWE)
- Fri 1/27 Lab: Homogenous rotating fluid, lack of vertical shear
- Mon 1/30 Rotating linear SWE on an f-plane: Poincare Waves
- Wed 2/1 NO CLASS
- Fri 2/3 More on Poincare Waves, Phase & Group Velocity, Interial oscillations
- [Midterm handed out, due 2/10]
- Fri 2/3 PV: Potential vorticity (linear SWE), Rossby Adjustment Problem
- Mon 2/6 Effects of horizontal boundaries: Kelvin waves, tides
- Wed 2/8 SWE PV conservation with topography: Taylor columns
- Fri 2/10 NO CLASS
4. Stratified flow
- Mon 2/13 Two-layer fluids
- Wed 2/15 Two-layer internal waves with stratification
- Fri 2/17 Energy: KE & APE (Boussinesq)
- Fri 2/17 Lab: Geostrophic adjustment with 2-3 layers
- Mon 2/20 HOLIDAY
- Wed 2/22 NO CLASS (Ocean Sciences Meeting)
- Fri 2/24 Continuous Stratification - Linear internal inertia-gravity waves (IGWs)
- Fri 2/24 IGWs continued ...
- Mon 2/27 IGWs continued ...
- Wed 3/1 IGWs and Flow over Topography
5. Forced motion
- Fri 3/3 Reynolds Averaging and the Ekman layer
- Fri 3/3 Lab: The Ekman layer and spin-down, IGW's
- Mon 3/6 Ekman pumping and spin-down
6. Advanced Topics
- Wed 3/8 Rossby waves on a beta-plane
- [Final exam handed out, due 3/15]
- Fri 3/10 Quasigeostrophic scaling
- Fri 3/10 Review Session and Evaluations
Assigments
Code
Breaking internal wave in clouds over campus.
Photo: Chaim Garfinkel