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

Tues/Thurs 10.30-11.50, and labs at 1.30 Wednesday, room 107 Ocean Sciences
Lectures in room 205 Ocean Teaching Building (OTB), labs in Ocean Sciences 107, the GFD lab .

Geophysical Fluid Dynamics - I - Winter 2015


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

Teaching Assistant:

Miguel Jimenez (
Ocean Sciences Building, 206-543-5214.
office hours: to be determined.

Homework & quizzes Bulletin Board Grades

Discussions Lecture notes Reading Assignments Homework Labs Observational Data Course description Prerequisites Outline (syllabus) Textbook Links

Mt. Rainier with wave clouds



In response to questions I've posted some notes on problems 2.7,2.8 of problem set 2 below (under Homework).

Our mid-term quiz will tentatively be handed out on Thurs 5 Feb as a take-home, to be returned Friday by noon. We will discuss possible conflicts in class this week.

Week 4 lecture notes for 1-layer geostrophic adjustment are posted below. This parallels Gill's treatment in Ch. 7 so far.

A Matlab m-file is posted under Lecture notes, which animates the 1-dimensional (η(x,t),u(x,t),v(x,t)) adjustment to an unbalanced initial height field (u=0=v at t=0). You can rewrite the initial η-field to mimick problems 2.7 and 2.8. A similar code of mine also plots the paths of fluid particles (seen from above): see figures at end of lectures 7,8 which show how near-inertial oscillations occur in the gravity/inertial waves emerging from the adjusting flow.


Reading for week 4 and Problem set 2 are posted below. I retooled it because we have not fully described geostrophic adjustment in class; I put a due date of Friday 30 Jan to give an extra day (if you can email or deliver it then; if logistically difficult see me).

Again we've asked you for this Thursday 22 Jan to write on one page (2 sides) notes on the readings for Coriolis effects without density stratification, mostly. This comes from reading and lectures and labs. Reading, posted below is mostly the same in Ch. 7 as assigned last week, but with two sections 7.9, 7.10 added (which are mostly review material). It would be good to include questions, impressions and possibly an example applying these rather abstract ideas to atmosphere and ocean flows, more than repeating equations from the text. Think about raising a question in class Thursday from your reading etc.

The 2d and 3d sets of lecture notes are now posted below.

Lab 3 this week will be on geostrophic flow and its development when the fluid is forced into motion in some way. Given that Coriolis effects push the fluid at right angles to its horizontal velocity, the pressure force that allows the fluid to break out of this constraint needs thought.


Problem set #1 is posted below (under 'homework'). In problem 1 an error has been corrected (in red). Due Tues 20 Jan.
We will continue spending some class time working out problems. This Thursday try to bring questions based on this week's reading (see below for that). This does not need to be handed in.

Slides from week 1 are now posted under 'lectures' below, and a typo was corrected in Week 1 lecture notes (in red font).
The grading policy is now shown under 'Grading' below.
This week's reading is posted below: continuing with basic equations and beginning Coriolis effects of the rotating Earth. In wlectures we will say some more about heat engines and convection, and the Earth's energy balance and then work on rotating Earth GFD.
A problem set is forthcoming, and we will try to do some of it during classtime.
Our 2d lab on Weds. 14 Jan (1.30-2.20) will be about Coriolis effects, angular momentum and geostrophic balance.


We scheduled the first lab for Wednesday 7 Jan at 1.30-2.20 in the GFD lab. Images and notes from this lab are posted below (linked under 'Labs' at the top of this page).

Lecture notes for Week 1 are posted below also (under 'Lectures'). These parallel the sections in Gill on thermodynamics and equations of state. Much of the detail has not been given in class, but this is meant to add extra ideas to your developing ideas of the thermal aspects of atmospheres and oceans.

With the two lecture meetings per week, 1.5 periods long, we will try to dedicate some time to in-class discussion. This week's 'assignment' is below under 'discussions'.

Observations of large-scale circulations (jet stream, storm track, cyclonic development (at the 1000km scale), ocean eddies and boundary currents) and smaller scale waves (internal ocean tides, which are internal gravity waves influence by Earth's rotation) were examples of GFD in action.

The weather loops are a good place to spend time: we looked at cold air outbreaks in the central US (this week's weather), which involve strongly developing waves in the jet stream, a low-pressure trough carrying frigid air to Texas, east of the Rocky Mountains. Rossby waves in the ocean take several different forms, one being the westward marching mesoscale eddies (~100km diameter) which are highly nonlinear waves: these we saw in satellite altimetry videos of the surface ocean currents of the Atlantic. The newly established global observing system for the oceans provides 'ground truth' for newly capable numerical models of the ocean circulation.

The mathematics used in GFD is important, yet in some cases the equations can be very simple, one example being the wave equation for Rossby waves/mesoscale eddies in the upper few hundred m of the oceans, where the same equation also describes the wind-driven gyre circulation of the ocean (the Sverdrup transport).

Thermodynamics is important yet often neglected in GFD textbooks. Of course there are thermodynamics books..a classic series being by Francis Sears (in library or Amazon). Dennis Hartmann's Global Physical Climatology is a very good introduction to atmospheric circulation related to thermodynamics, moist and dry, and radiation. We don't have time for more than the brief introduction and one lab unfortunately, but I hope the important ideas of heat engines, 1st- and 2d law of thermodynamics introduced there will help in understanding the buoyancy effects of GFD.

On this website lecture material will be posted, which gives an independent treatment of GFD in parallel with Gill's (and Vallis') textbook sections.

First class: 10.30 Tuesday Jan 6, 2015 in Room 205 Ocean Teaching Building.

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 and Greg Hakim (5th Ed., Academic Press 2013).
    • An Introduction to Geophysical Fluid Dynamics - 2d Edition: Physical and Numerical Aspects by Benoit Cushman-Roisin & Jean-Marie Beckers (Internat'l Geophysics 2011).
    • 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),
    • Global Physical Climatology by Dennis Hartmann (Academic Press);
    • 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).
    • Thermodynamics, while not a major activity in this course, is important. An excellent text is Thermodynamics, Kinetic Theory and Statistical Thermodynamics, by Francis Sears and Gerhard Salinger.
    • On the same subject, an introduction by a Nobel laureate physicist is Thermodynamics by Enrico Fermi, (Dover!)

    Vallis' text is available as a .pdf for your laptop or Kindle or IPad, for $80 here. 

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    Reading Assignments

    Lecture notes
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    • Thurs 8 Jan
      Write down (on no more than one piece paper) notes on your impressions, questions, examples relating to the following. Add notes to it during class and hand in as you leave. These could be bullet points or descriptive paragraphs. Better to concentrate on one or two than do all three.

      In reading Gill's sections in Ch.3 and 4 on thermodynamics and the basic equations of motion, prepare questions for discussion in 3 areas:
      o Energy equations, particularly focusing on how the internal thermodynamic energy (1st law of thermo) and the external mechanical energy (KE and PE, kinetic and potential energy) interact. How do they interact, and what are examples in atmos and ocean?
      o The geopotential field: what is it and how does it combine true gravity and effects of being on a spinning planet?
      o Potential temperature: how is it derived and how does it appear in equations of state for an ideal gas?

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    Observational Data
        Ocean data
        Atmosphere data

    GFD Labs
    Here are pdf's showing some (not all) the happenings in our lab hours.

    Homework and Quizzes

    Course outline (syllabus)


    The class grades will be calculated from:
    problem sets and class exercises - 50%
    mid-term quiz - 20%
    final exam - 30%

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  • Office hours: see me after class any day, or by appointment at another time. Miguel Jimenez's office hours will be announced soon.

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    Course description Geophysical Fluid Dynamics (GFD) is the fluid dynamics of the atmosphere and oceans. It centers on fluids which have active buoyancy effects through variations in their mass density. It also centers on the effects of the rotating planet: we live on an accelerating frame of reference which affects ordinary Newtonian physics. Finally our planet is nearly spherical, so ideas based on the usual rectangular, Cartesian coordinates will have to change. While our planet of interest is Earth, in the spirit of 'taking a trip so as to undertand better your homeland', GFD applied to Jupiter's deep atmosphere and the liquid iron core of the Earth teaches us about Earth's air and water themselves.

    GFD-1 carries on fairly continuously from Fluid Dynamics, AtmosSci505/AMath505/Ocean511, Fall 2014. We will revisit much of that material so keep Prof. Bretherton's notes handy.

    We will be setting up a GoPost bulletin board. We have not made much use of GoPost in the past, but it may be worth developing this year, for online discussions.

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    Prerequisite courses for GFD-1
    AS505/OC511 Fluid Dynamics or equivalent (consult with instructor).

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