12.810 Dynamics of the Atmosphere

Graduate; Spring
(Spring '09: Lectures MW2-3:30, Rm 54-317)

Instructor: Alan Plumb, 54-1712, x3-6281, rap@rossby.mit.edu
Prereq.: 12.800
Units: 3-0-9

Topics, notes, and reading lists

0. Overview

Handout notes:
Overview of the observed global atmosphere

1. Zonally symmetric circulations

General Material:
Lindzen, Dynamics in Atmospheric Physics, Chapter 7

Specific Papers:
Held & Hou, J. Atmos. Sci., 37, 513-533 (1980) present the theory, and numerical simulations, for the case of thermal forcing symmetric about the equator. Lindzen & Hou, J. Atmos. Sci., 45, 2416-2427 (1988) extended the theory to a solstice-like case, when thermal forcing is not symmetric about the equator; they found that a small asymmetry in the forcing could produce a large asymmetry, an strong amplification, in the response. However, Dima & Wallace, J. Atmos. Sci., 60, 1522-1527 (2003) showed from the reanalysis data that the seasonal cycle of the Hadley cells is rather smooth, and gives little if any evidence of such sensitivity in practice. Walker & Schneider, Geophys. Res. Lett., 32, L06813, doi:10.1029/2004GL022304 (2005), on the basis of 3D model experiments, question how well the 2D theory actually explains the parameter dependencies when eddies are present.

The possibilty of threshold behavior associated with violation of Hide's theorem in axisymmetric monsoon-like situations was discussed in Plumb & Hou, J. Atmos. Sci., 49, 1790–1799 (1992); Emanuel, J. Atmos. Sci., 52, 1529–1534 (1995) explicitly included moisture to show the importance of the distribution of subcloud entropy (which controls the radiative-convective equilibrium temperature). Prive & Plumb, J. Atmos. Sci., 64, 1431-1442 (2007), addressed the (limited) degree to which the axisymmetric theory applies to more realistic 3D monsoon circulations.

Handout notes:
Theory of the Hadley circulation

2. Internal gravity 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

A numerical simulation by Dale Durran (U. Washington) of the "St Andrews' cross" (with a nice zoom-in, showing velocities) can be found here. WKB analysis is discussed in detail in (e.g.) Chapter 10 of: Bender & Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978. Internal gravity wave breaking is discussed in: Lindzen, J. Geophys. Res., 86, 9707-9714 (1981), and application of the theory to parameterization in GCMs in: Palmer et al., QJRMS, 112, 1001-1039 (1986).

Handout notes:
Simple wave properties: Boussinesq case
Simple wave properties: compressible case
Mountain waves and vertical propagation
Heat and momentum transport by internal gravity waves (updated 3/4/09)

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

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

The movie clip of the lab Rossby wave demonstration (MPEG; file size is 11MB) can be found here

The "original" Rossby wave paper is: Rossby, J. Mar. Res., 2, 38-55 (1939). The classic paper on vertical propagation is: Charney & Drazin, J. Geophys. Res., 66, 83-110 (1961). Effects of spherical geometry on Rossby wave propagation are described (using explicit modeling) in Grose & Hoskins, J. Atmos. Sci., 36, 223-234 (1979), and (using ray tracing in longitude/latitude) in Hoskins & Karoly, J. Atmos. Sci., 38, 1179-1196 (1981) and (using ray tracing in latitude/height) in Karoly & Hoskins, J. Meteor. Soc. Japan, 60, 109-123 (1982). Use of the refractive index to describe Rossby wave propagation was pioneered by Matsuno, J. Atmos. Sci., 27, 871-883 (1970). A good review of stationary Rossby wave theory is the article by Held in Large-scale Dynamical Processes in the Atmosphere, Academic Press, London; New York: 127-168 (1983).

The Rossby wave critical layer is discussed in Haynes, J. Fluid Mech., 161, 493-511 (1985). The movie of SST from the zonally re-entrant ocean model, showing a very clear example of critical layer transport, is here.

Handout notes:
"Equivalent barotropic" (shallow water) flow; Rossby waves
Baroclinic Rossby waves; external mode; vertical propagation (amended)
Spherical geometry effects and breaking

4. Wave conservation properties and stability of zonal flows

General material
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 original derivation of the Eliassen-Palm theorem, in the special case of conservative waves of steady amplitude, was given in Eliassen & Palm, Geofys. Publ., 22(3), 1-23 (1961). Extensions to include non-steadiness and non-conservative effects were by Boyd, J. Atmos. Sci., 33, 2285-2291 (1976); Andrews & McIntyre, J. Atmos. Sci., 33, 2031-2048 (1976). One of the first calculations of climatological Eliassen-Palm fluxes was in Edmon et al., J. Atmos. Sci., 37, 2600-2616 (1980).

The Charney-Stern stability theorem was introduced by Charney & Stern, J. Atmos. Sci, 19, 159-172 (1962).

Handout notes
QG wave conservation properties and stability of zonal flows

5. Baroclinic instability

General material
This topic is covered in many GFD and atmospheric dynamics texts, e.g., Holton, Chapter 8. A particularly thorough discussion (which goes into more depth than we shall) is Pedlosky, Chapter 7.7.
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. When applied locally, details can be over-interpreted (Plumb, J. Atmos. Sci., 40, 1670-1688, 1983) but we will avoid these pitfalls by focusing exclusively on integrated budgets.

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

6. Tropical wave dynamics

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). The "Gill model" of the atmospheric response to localized tropical heating was introduced by Gill, Quart. J. Roy. Meteor. Soc., 106, 447-462 (1980). Reinterpretations of the Gill model include Lindzen & Nigam, J. Atmos. Sci., 44, 2418–2436 (1987); Neelin, J. Atmos. Sci., 46, 2466-2468 (1989); and Neelin & Zeng, J. Atmos. Sci., 57, 1741-1766 (2000). Observations of convectively coupled equatorial waves are described in Wheeler & Kiladis, J. Atmos. Sci., 56, 374-399 (1999). Easterly waves are described in (e.g.) Thorncroft et al., Quart. J. R. Meteor. Soc., (1994)

Handout notes
Equatorial waves in shallow water
The continuous case: vertical structure of equatorial waves
Climatology of the tropics (PowerPoint)
The Gill model

7. The general circulation

Discussion of how the mean state responds to baroclinic eddy fluxes can be found in Robinson, J. Atmos. Sci., 51, 2553 (1994)

Handout notes
General circulation

Problem Sets

Problem Set 1 (due 2 March) Questions Sample answers
Problem Set 2 (due 18 March) Questions Sample answers
Problem Set 3 (due 15 April) Questions Sample answers
Problem Set 4 (due 29 April) Questions Sample answers
Problem Set 5 (due 13 May) Questions

Alan Plumb
Last updated 12 May 2009