ATOC 5061, Fall 2010

ATOC 5061: Dynamics of Oceans
Or, Waves in Oceans.
Explores theories of the large-scale ocean, including quasigeostrophic, planetary geostrophic, and shallow water equations. Topics may vary to focus on ocean climate (e.g. thermocline, westward intensification), ocean waves (e.g. gravity, Rossby, and Kelvin), or ocean models (toy, analytic, and numerical). May be repeated up to 9 total credit hours. Prereqs., ATOC 5400 and ATOC 5051 or 5060 or equivalent.

In Spring 2009, the focus was mainly on ocean models, doing some hands-on numerical modeling of simple models, waves, and shallow water equations, as well as discussing toy and analytic models. Fall 2010 will focus more on ocean waves, instabilities, eddies, and wave-mean interaction, but we'll still use some simple numerical models to illustrate.

You can access the syllabus and class notes.

Class Meetings and Notes

Class meets Tuesday and Thursday 1:00-2:15 (changed after first meeting) in Ekeley W240. All assignments due at the beginning of class on day noted. Office Hours are by appointment.
You can subscribe to a google calendar called "ATOC5061: Dynamics of Oceans" for reminders of dates and assignments.
Wk Reading

Large Print=Required, Small=Optional
Tuesday Thursday Assignment
(Due 1:00PM on Date)
1 Notes Part II, Vallis15.3
Linear Classification: Strogatz5.
Chaotic Pendulum: Shinbrotetal92
Box Model: Stommel61
8/24: Oscillators and Chaos: The Double Pendulum 8/26: Linear and Nonlinear Perturbations: Stommel Box Model Due 9/2: CULearn Assignment 1
2 Vallis3.1
Dimensional Analysis: Notes Part I, Wilcox2
Waves: C-R&B Appendix B, Henderschott1
8/31: Dimensional Analysis, Nondimensional Equations. Boussinesq, Hydrostatic approximations. 9/2: Wave Kinematics Due 9/9: CULearn Assignment 2
3 Henderschott1, Henderschott3, Notes Chp. 4 9/7: 1d Surface Waves 9/9: 1d Surface Waves & Spectra Due 9/23: CULearn Midterm 1, Answer Key
4 9/14: No Class 9/16: No Class Due 9/23: CULearn Midterm 1, Answer Key
5 C-R&B13, Henderschott4 9/21: Nonlinear 1d Waves: Stokes Drift, Stokes Series, and KdV 9/23: 2d x-z Waves: Internal Gravity Waves Due 9/30: CULearn Assignment 3
6 Vallis2.1-2.3, 3.1-3.6 9/28: 2d x-z Waves: Internal Gravity Waves, Shear Instabilities, & Spectra 9/30: 2d Rotating Shallow Water Eqtns Due 10/7: CULearn Assignment 4
7 C-R&B9.1-9.6, Henderschott5 10/5: 2d SWE Waves: Plane Waves, Sverdrup Waves, Inertial Oscillations 10/7: 2d Channel Waves: Poincare, Kelvin Due 10/14: CULearn Assignment 5
8 Pedlosky3.1-3.11 10/12: 2.5d Reduced Gravity, Geostrophic Adjustment 10/14: 2.5d Reduced Gravity, Geostrophic Adjustment, Rossby Waves Due 10/21: CULearn Assignment 6
9 Vallis5.1-5.3 10/19: 2&2.5d Waves in Beta-Channel 10/21: 2.5d PG Waves in Beta-Channel Due 11/9: CULearn Midterm 2
10 Fox-Kemper & Ferrari 10/26: 2.5d PG Wave-Mean Interaction in Channel 10/28: 2.5d PG Waves in a Box: Parsons Model, Basin Spin-up, Wave-Mean Interaction Due 11/9: CULearn Midterm 2
11 Vallis5.3 Pedlosky3.12-3.25, Fox-Kemper & Pedlosky 11/2: 2.5d QG Waves in a Channel 11/4: 2d QG Waves in a Basin, Equilibration of Inertial Munk Models
12 Vallis5.4-5.8 11/9: 3d QG and SQG 11/11: 3d QG Waves Due 12/2: CULearn Assignment 7
13 Vallis6 Nakamura, 93 11/16: Barotropic and Shear Instability 11/18: Baroclinic Instability Due 12/2: CULearn Assignment 7
14 Fall Break Fall Break Fall Break Fall Break
15 Vallis7 11/30: 3d QG: The Eliassen-Palm Flux 12/2: The Transformed Eulerian Mean and Nonacceleration Theorem Due 12/15: CULearn Final
Final Key
16 Vallis7 12/7: QG: Wave-Mean Interaction in 3d 12/9: Summary Due 12/15: CULearn Final
Final Key
17 Exam Week Exam Week Exam Week Exam Week

Web Resources and Texts

Course Specific



  1. Course Notes
  2. Chapman and Malanotte-Rizzoli's Notes on Henderschott's Wave Motions in the Ocean
  3. Cushman-Roisin & Beckers, Intro. to GFD
  4. Pedlosky, Waves in the Ocean and Atmosphere
  5. LeBlond & Mysak, Waves in the Ocean
  6. Vallis, Atmospheric and Oceanic Fluid Dynamics


  1. Pedlosky, GFD
  2. Pedlosky, Ocean Circulation Theory
  3. Salmon, Lectures on GFD
  4. Djikstra, Nonlinear Physical Oceanography
  5. McWilliams, Fundamentals of GFD
  6. Greenspan, The Theory of Rotating Fluids
  7. Zeitlin, Nonlinear Dynamics of Rotating Shallow Water
  8. Batchelor, An Intro. to Fluid Mechanics
  9. Batchelor, The Theory of Homogeneous Turbulence
  10. Kundu, Fluid Mechanics

Software and Toolkits

  1. Matlab Download Instructions
  2. Matlab File Exchange

The Models

  1. Simple Harmonic Oscillator
  2. Chaotic Pendulum
  3. Stommel Box Model
  4. 1d Linear Surface Gravity Waves
  5. 1d Shallow Water Equations
  6. Inertial Oscillator
  7. 2d Shallow Water Waves
  8. 2d Shallow Water Wave w/ betas
  9. 2d shallow water eqtns w/ beta in a box(matlab)
  10. Wind-Driven Gyres
  11. Eady/Charney
  12. 2-layer QG Turbulence
  13. Point Vortices
  14. Hetons
  15. The Unified Oscillator
  16. Gnanadesikan's MOC

Additional Fun Reading


  1. Cook, The Three Voyages of Captain James Cook Round the World, Vol. 1.1, 1.2, 2.1, 2.2, 3.1, 3.2, 3.3.
  2. Maury, 1860: The Physical Geography of the Sea and Its Meteorology
  3. Darwin, The Voyage of the Beagle
  4. Darwin, The Structure and Distribution of Coral Reefs
  5. Sverdrup, New Land: Four Years in the Arctic Region
  6. Nansen, Farthest North, Vol 1 and Vol 2.
  7. M'Clintock, The Voyage of the Fox in the Arctic Seas
  8. Bowditch, The American Practical Navigator
  9. Philander, Our Affair with El Nino
  10. Emanuel, Divine Wind: The History and Science of Hurricanes


  1. Dana, Two Years Before the Mast
  2. Defoe, Robinson Crusoe
  3. Homer, The Odyssey
  4. London, The Sea Wolf
  5. Melville, Moby Dick
  6. Stevenson, Treasure Island
  7. Verne, 20,000 Leagues Under the Sea

CU Specific Guidelines

  1. Disability Accomodations
  2. Religious Observance
  3. Classroom Behavior, *Note* Prof. Fox-Kemper regards inappropriate cellphone and laptop use as disruptive behavior.
  4. Student Code
  5. Discrimination & Harrassment
  6. Honor Code: here and here.