ATM S 509/OCEAN 512     SLN: 1548 (ATM), 6180 (OCN)

MWF 10:30-11:20, and 2.30pm on Thursdays for labs and problem solving sessions.
Lectures in ATG 310c (Atmospheric Sciences), labs in Ocean Sciences 107, the GFD lab . Note, we may shift lectures to JHN 022 if construction noise is too extreme in ATG310c.

Geophysical Fluid Dynamics - I - Winter 2011


Professor P.B.Rhines
Ocean Sciences Building 319
tel: 543-0593
office hours: MW after class, and by appointment.

Teaching Assistant:

Alison Gray (
Ocean Sciences Building 325D.
office hours: T 2:30-3:30, Th 10-11, and by appointment.

Homework & quizzes ø Bulletin Board Grades

Observational Data Course description Prerequisites Outline Textbook Reading Assignments Lecture notes Labs Homework Links


Lab #8 jetstreams and eddies

Above: internal gravity waves generated by an oscillating cylinder, with uniform stratification (Lab #6 UW-GFDlab, 17 Feb 2011).

(1st image above) Space-time (x-t) plot of surface elevation for short, non-hydrostatic gravity waves in a 1-layer model, propagating away from an initial 'lump' of elevation. Time is the vertical axis, x is the horizonatal axis. Note how dispersion (variation of group- and phase-velocity (Cg and Cp) with wavelength) creates the 'pebble in the pond' effect. Here the long waves have larger Cg and Cp and Cp is 2x Cg.
(2d image above) Three x-t diagrams for long, hydrostatic waves with rotation (f). 1-layer model, surface elevation plotted. The left panel has f=0, the middle panel is moderate f. In terms of the Rossby deformation radius R\subd = Co/f, this is L ~ Rd, where L is the width of the initial 'hump' of surface elevation. The righthand panel has L >> Rd, so that the waves are mostly near-inertial (frequency close to f) and there is a persistent ridge of geostrophic flow trapped near the initial hump.
Note that these are plots of the theoretical solutions, not numerical models. The two techniques are complementary; theory can give you general answers, while models can include more realistic detail, and can solve more difficult (e.g., nonlinear) problems.
(3d image above): perspective plot of x-t Hovmoeller plot of free-surface elevation Η for geostrophic adjustment from an initial state with zero velocity and a Gaussian bell-curve 'hump' of Η. The waves are close to the inertial frequency (hence have small group velocity) and the mean flow emerging is a double jet in the y-direction, in geostrophic balance.

While 1-layer models seem unlike either ocean or atmosphere, their horizontal space-time structure is nearly identical to the fully stratified model, for each vertical (~cos mz-) mode. Thus one can understand a wide range of atmosphere/ocean geostrophic adjustment from these beginnings. Following this UW GFD-1 course, the various GFD-2 courses introduce the evolution of geostrophically balanced flows in Rossby waves, baroclinic instability, geostrophic turbulence => general circulation.
(4th image above): contours of 250HPa jet-stream level dynamic height (colors, blue = low, red = high), and 30HPa stratospheric dyanamic height showing the much more symmetrical polar cyclonic vortex in wintertime. Using m_map projection 'satellite' with Matlab. Such images are easily animated.


WEEK 10: Mon 7 March 2011
WEEK 9: Weds 2 March 2011
WEEK 8: Sunday 20 Feb 2011 WEEK 2:
The homework (due Friday)is posted with added comments in red font.
Reading assignment is below. Lectures to date are posted. Syllabus (outline) is posted.
We hope to have a lab on Thursday about rotation; Coriolis and angular momentum.


We will ask you to describe:
  • Your fluid dynamics background (courses etc)
  • Your math background
  • Your Matlab experience level (likely greater than ours!).
  • What would you like to get out of this GFD course?


    Atmosphere-Ocean Dynamics by Adrian Gill (Academic Press 1982) is our primary text. We have a 'suggested' text, Atmospheric and Oceanic Fluid Dynamics by Geoffrey Vallis (Cambridge University Press, 2006), which is not required. Vallis' text is newer and includes many modern topics, particularly involving vorticity dynamics of synoptic-scale flows. We will give a list of useful sections in Vallis that parallel our lectures and Gill's text.

    There are in addition other fluid dynamics and GFD textbooks and each has its merits:

    • An Introduction to Dynamical Meteorology by James Holton (4th Ed., Academic Press 2004).
    • Geophysical Fluid Dynamics by Joseph Pedlosky (Springer Verlag),
    • sections in Fluid Dynamics by Pijush Kundu and Ira Cohen (4th Edition, Academic Press),
    • Lectures on Geophysical Fluid Dynamics by Rick Salmon (Oxford University Press),
    • Introduction to Circulating Atmospheres by Ian James (Cambridge University Press 1994),
    • Waves in Fluids by James Lighthill (Cambridge University Press, 1978),
    • An Informal Introduction to Theoretical Fluid Mechanics by James Lighthill (Clarendon/Oxford University Press 1986),
    • Fluid Mechanics, 2d Edition by L.D. Landau and L.M. Lifshitz (Butterworth-Heinemann div or Reed Publishing, Ltd. 1959-2000),
    • Atmosphere, Ocean and Climate Dynamics, an Introductory Text by John Marshall and Allan Plumb (Elsevier Academic Press, 2008);
    • Fundamentals of Atmospheric Physics by Murray Salby (Academic Press, 1996).

    Vallis' text is available as a .pdf for your laptop or Kindle or IPad, for $60 here. 

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    Reading Assignments

    Week 1 Read Gill: from Chapter 3 and 4 (omitting some sections):

    It would be good to review Lectures 1,2,3 from the fall Fluids course, . Chap. 1 of Kundu has similar material to the above sections of Gill and Vallis.

    Week 2

    Week 3

    Week 4

    Week 5

    Weeks 6-7

    Week 8

    Week 9

    All Gill sections read so far:
    Lecture notes
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    Observational Data