Large-scale Ocean and Atmosphere Dynamics

Course number: 16:712.502

Credits: 3

Instructors: Haidvogel and Levin

Term offered: Spring 2008 / alternate years

Prerequisites: 16:712.501 (or equivalent)

1. Brief Course Description

2. Course Outline

3. Texts

4. Other References

5. Criteria for Student Grading

6. Homeworks

7. Lecture Notes

1. Brief Course Description

The theoretical basis for the observed large-scale, atmospheric and ocean circulation is presented. Topics include: derivation of the three-dimensional equations of motion; vorticity and energy; the planetary boundary layer; synoptic-scale motions; linear waves; hydrodynamic instability; the general circulation on the sphere; the effects of boundaries on large-scale horizontal flow; and vertical structure and motion.

2. Course Outline (approximate):

a. Introduction (1/22; Haidvogel)

b. Derivation of the equations of motion (1/24, 1/29, 1/31; Levin): Derivation of the "complete" inviscid equations on a rotating earth; the primitive equations: the traditional, Boussinesq and hydrostatic approximations

c. Vorticity and Energy (2/5, 2/7; Levin): The circulation theorem; vorticity and planetary vorticity; Ertel potential vorticity; kinetic and potential energy equations

d. The Planetary Boundary Layer (2/12, 2/14, 2/19; Levin): Turbulent kinetic energy; Reynolds averaging; the closure problem; the mixing length hypothesis; the Ekman layer; the log layer; higher-order closure schemes

Exam 1 (2/21; review on 2/19)

e. The general circulation on the sphere ( 2/26, 2/28; Levin): The zonally averaged circulation; the angular momentum budget; low-frequency variability; mean-eddy energy cycles

f. Synoptic-scale motions (3/4, 3/6, 3/11; Haidvogel): Scaling the equations for large-scale, mid-latitude flow; quasi-geostrophy; the beta plane; static structure of the ocean and atmosphere

g. Linear waves (3/13, 3/25; Haidvogel): The shallow water equations; properties of waves; inertial, gravity, and inertio-gravity waves; Rossby waves

h. Hydrodynamic instability (3/27, 4/1; Haidvogel): Instability in a one-layer system; the two-layer model; baroclinic instability; energetic considerations; instability in a continuously stratified fluid

Exam 2 (4/3; review 4/1)

i. The wind-driven ocean (4/8, 4/10, 4/15; Levin): Sverdrup flow; linear; frictional boundary layer theories; the inertial problem; integral balances; effects of boundaries on waves

j. Vertical structure and motion (4/17, 4/22; Haidvogel): Source-sink driven flows on the sphere; homogenization of potential vorticity; the oceanic thermocline; effects of topography

k. The effects of topography (4/24, 4/29; Haidvogel): Taylor columns/caps, mean flow rectification

Exam 3 (5/1; review on 4/29)

3. Texts:

Holton, J. R., 1992: An Introduction to Dynamic Meteorology;

Academic Press, New York; Third Edition; 511 pp.

4. Other References:

Batchelor, G.K. 2000: An Introduction to Fluid Dynamics;

Cambridge University Press; 635 pp;

Gill, A.E. 1982: Atmosphere-Ocean Dynamics;

Academic Press; 662 pp;

Haidvogel, D.B., Beckman, A. 1999: Numerical Ocean Circulation Modeling; Imperial College Press; 300 pp;

Haltiner, G.J., Williams, R.T. 1980: Numerical Prediction and Dynamic Meteorology; John Wiley & Sons; 477 pp;

Kantha, L.H., Clayson, C.A 2000: Small-scale Processes in Geophysical Fluid Flows; Academic Press; 888 pp;

Pedlosky, J. 1998: Geophysical Fluid Dynamics;

Springer-Verlag, Second Edition; 728 pp;

Pedlosky, J. 1998: Ocean Circulation Theory;

Springer-Verlag, New York; Second printing of First Edition (1996); 453pp.

5. Criteria for Student Grading:

§ homework sets (4@ 10%)

§ written exams (3@ 20%)