12.333 Dynamics of the Atmosphere
Spring '14: Lectures TR 11-1230, Rm 54-823
(Class meets with 12.810)
Instructor: Alan Plumb, 54-1712, x3-6281, firstname.lastname@example.org
Assessment will be based on:
- Problem sets (one every 2 weeks) (60% of grade)
- A final exam (40%).
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.
Overview of the observed global atmosphere
1. The circulation of a zonally symmetric atmosphere
of the axisymmetric Hadley circulation
Background material on the Boussinesq approximation
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,
James, Introduction to Circulating Atmospheres, Chapter
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
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.]
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
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
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.
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
Instability of the zonal flow; genesis of midlatitude storms
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
5. Tropical circulations
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)
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
Role of Eddies in the General
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 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
Last updated 2014 May 16