12.333 Dynamics of the Atmosphere

Graduate; Spring
Spring '14: Lectures TR 11-1230, Rm 54-823
(Class meets with 12.810)
Prereq.: 12.003
Units: 3-0-9

Instructor: Alan Plumb, 54-1712, x3-6281, plumb@mit.edu

Assessment will be based on:

Topics, notes, and reading lists

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 shall reference most frequently is: Holton, J.R., An Introduction to Dynamic Meteorology, 4th edition, Elsevier Academic Press (Int. Geophysics Series, vol. 88), 2004.

0. Overview

Handout notes:
Overview of the observed global atmosphere

1. The circulation of a zonally symmetric atmosphere

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;
James, Introduction to Circulating Atmospheres, Chapter 4;
Vallis, Atmospheric and Oceanic Fluid Dynamics, Chapter 11.

Later in the class, we will address limitations of this zonally symmetric theory as a model of the real world; specifically, eddies play a significant role in the real atmosphere.

2. Internal gravity waves

Handout notes:
Internal gravity waves
Background material on pressure coordinates.
Background material on 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.]

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

Handout notes:
I: Large-scale flow, potential vorticity and Rossby waves in a shallow water system..
Here are some notes on the shallow water equations.
II: 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 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. Instability of zonal flows

Handout notes
Instability of the zonal flow; genesis of midlatitude storms

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

More detail and further reading:
It is difficult to find source material for wave conservation and the stability constraint that does not go much deeper than we do. 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.)

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.

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

5. Tropical circulations

Handout notes
Climatology of the tropics (slideshow)
Equatorial waves; response to stationary localized forcing: the Gill model; the Walker circulation and monsoons
El Nino and the Southern Oscillation (slideshow)

General material
Much of what we will discuss (except for details of the Gill model) is covered in Holton, Chapter 11. The early definitive study of equatorial waves is by Matsuno, J. Meteor. Soc. Japan, 44, 25-43 (1966), and the theory is extensively covered in Gill, Atmosphere-Ocean Dynamics, Academic Press (1982). Observations of convectively coupled equatorial waves are described in Wheeler & 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 (pdf or ppt) on current status is available from the Climate Prediction Center of the National Weather Service (choose "Weekly ENSO update", pdf or ppt).

6. The general circulation

Handout notes
Role of Eddies in the General circulation

General material
Discussion of how the extratropical mean state responds to baroclinic eddy fluxes, including how the impact of eddies on the upper tropospheric zonal flow depends on thermal adjustment rates and surface friction, can be found in Robinson, J. Atmos. Sci. (2001).

Problem Sets

Problem Set 1 Axisymmetric Hadley circulations (due March 3). Sample answers
Problem Set 2 Internal gravity waves (due 20 March). Sample answers
Problem Set 3 Vorticity and Rossby waves (due 17 April; extended to 24 April).Sample answers
Problem Set 4 Waves, fluxes and stability (due 8 May).Sample answers

Alan Plumb
Last updated 2014 May 16