12.333 Atmospheric Dynamics

Undergraduate; Spring
(Spring '12: Lectures TR 11 - 12:30; Rm 54-317)
(Course meets with 12.810)

Instructor: Alan Plumb, 54-1712, x3-6281, plumb@mit.edu
Prereq.: 12.003
Units: 4-0-8

Assessment will be based on:

Course materials:


There is no set text for the class. Formal class notes will be handed out, and made available on this page. Reference to published source material will be made as appropriate. The text we will reference most frequently is:
Holton, J.R., An Introduction to Dynamic Meteorology, 4th edition, Elsevier Academic Press (Int. Geophysics Series, vol. 88), 2004.

Overview

Handout notes:
Overview of the observed global atmosphere


1. Theory of the Hadley circulation

Handout notes:

Theory of the axisymmetric Hadley circulation

Background material on the Boussinesq approximation

Other descriptions:
A broad (but not very deep) discussion of Hadley cell dynamics can be found in Marshall & Plumb, Atmosphere, Ocean and Climate Dynamics, Chapter 8 (up to and including Section 8.2.1).

More in-depth discussions of the Held-Hou theory are presented in Lindzen, Dynamics in Atmospheric Physics, Chapter 7, and in James, Introduction to Circulating Atmospheres, Chapter 4.


2. Internal gravity waves

[Aside: Dispersive and nondispersive waves. The movie clip showing a propagating wave packet, and illustrating the distinction between phase and group velocity, is here. It shows a Gaussian packet about 7 wavelengths wide of small-amplitude surface waves, with carrier wavenumber k = 1/D, on deep water of mean depth D.]

Handout notes:
Internal gravity waves in Boussinesq and compressible fluids
Mountain waves
Momentum transport by internal waves

General Material:
Gill, Atmosphere-Ocean Dynamics, Sections 6.4-6.5.
Lindzen, Dynamics in Atmospheric Physics, Chapter 8.
Holton, An Introduction to Dynamic Meteorology, Sections 7.4 and 9.4.

More detail and further reading::
Movies of the "St Andrew's Cross" demonstrations in the lab can be found on the Kyoto Uni. GFD web site (click on "Internal Gravity Wave" and then explore). A numerical simulation by Dale Durran (U. Washington) of the "St Andrews' cross" (with a nice zoom-in, showing velocities) can be found here.

There is a large body of literature on mountain waves; some recent examples can be found in the bibliography on Dale Durran's web site.


3. Large-scale flow: PV dynamics and Rossby waves

[Asides: The shallow water equations ; vorticity and circulation]

Handout notes:
Large-scale flow, potential vorticity and Rossby waves in a shallow water system.
Large-scale flow, quasi-geostrophic potential vorticity and Rossby waves in the atmosphere.


General material
Holton, An Introduction to Dynamic Meteorology, Sections 7.7 and 12.3

More detail and further reading::
The latest 500hPa analysis can be found on the EAPS synoptic lab. web site . The movie clip of the lab Rossby wave demonstration can be found here. A comprehensive presentation of a similar experiment -- the experimental setup, theory, and results -- from the Weather in a Tank Project can be found here.


4. Wave conservation properties and stability of zonal flows

Handout notes
QG wave conservation properties and stability of zonal flows

More detail and further reading:
It is difficult to find source material for much of this section that does not go into way too much theoretical depth for our purposes. The Charney-Stern stability theorem was introduced by Charney & Stern, J. Atmos. Sci, 19, 159-172 (1962). (They did not use the same language that we do, but the math is essentially the same.)


5. Baroclinic instability and extratropical storms

Handout notes
Violation of the stability constraint, and the Eady problem.

General material
This topic is covered in many GFD and atmospheric dynamics texts, e.g., Holton, Chapter 8.

More detail and further reading
The original presentation of the "Eady problem" is Eady, Tellus, 1, 33-52 (1949). The problem has subsequently been re-analyzed many times.
John Marshall's baroclinic instability movie (from 12.307) can be found here. Movies of baroclinic waves (in 3 different regimes) can be found on the Kyoto Uni. GFD web site (choose low resolution unless you have a fast connection).

Lorenz, The Nature and Theory of the General Circulation of the Atmosphere, WMO, Geneva (1967) discusses atmospheric energetics in some detail.


6. Tropical wave dynamics

Handout notes
Climatology of the tropics
Equatorial waves
Zonally asymmetric circulations: the Gill model
El Nino and the Southern Oscillation

General material
Much of what we will discuss (except for details of the Gill model) is covered in Holton, Chapter 11. Observations of convectively coupled equatorial waves are described in Wheeler and Kiladis, J. Atmos. Sci., 56, 374-399 (1999). An extensive discussion of Hermite polynomials and Hermite functions (both the "physicists' version" which we use, and the "probabalists' version") can be found in their Wikipedia entry. (This page also gives references to the more conventional lierature.)

The "Gill model" of the atmospheric response to localized tropical heating was introduced by Gill, Quart. J. Roy. Meteor. Soc., 106, 447-462 (1980).

NOAA has a usfeul and comprehensive web page on many aspects of ENSO, both general and current. The presentation on current status is available from the Climate Prediction Center of the National Weather Service (choose "Weekly ENSO update", pdf or ppt).


7. The general circulation



Problem Sets

Problem Set 1 (due Feb 28). Sample answers
Problem Set 2 (due Mar 15). Sample answers
Problem Set 3 (due Apr 19).
Problem Set 4 (due May 10).





R. Alan Plumb
Last updated 2012 May 10