## Instructor: |
Professor P.B.Rhines Ocean Sciences Building 319 tel: 543-0593 rhines@washington.edu office hours: after class, and by appointment. |
## Teaching Assistant: |
Miguel Jimenez (jimenezm@uw.edu) 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.

*
WEEK 3: *

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.

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 atmos.washington.edu 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:

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 1956...cheap!)

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

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**Reading Assignments**

*Week 4*

Gill sections on stratified geostrophic flow: 7.7, 7.8, 7.11, 7.12, and Kelvin waves, 10.4. (similar to Vallis sections 2.8, 2.9, 3.1, 3.6-3.8)*Week 3*

The same Gill sections 7.1 - 7.6 on Coriolis effects with 'Geostrophic Adjustment', which is the development of geostrophic flow from and initially 'unbalanced' initial condition. This is a key idea in GFD. Then add only sections 7.9 and 7.10 which are more or less review of circulation and vorticity, and introduction of potential vorticity including the planetary rotation contribution, f = 2Ω sinφ.*Week 2*- Gill 4.5 (4.5.1 especially), 5.1-5.2, 5.6-5.7, and head toward 7.1-7.6 which will carry on into the next week.
- Bretherton notes for review: Lec 4,5 (math review), Lecs 6,7,9 (equations of motion); Lec 10 (energy equation).
- parallel sections in Vallis: 2.1, 2.2

*Week 1*Read Gill: from Chapter 3 and 4 (omitting some sections):- 3.1-3.3, 3.5, 3.7
- most of Ch. 4 (omit rotation, 4.5.1 and spherical coordinates 4.12, for now).

{ Chaps. 1 and 2 of Gill are very nice, yet they have been covered in earlier courses for most people. Read these fairly quickly.} - Parallel sections in Vallis: Chap.1 up to p37 (up through Sec. 1.71) and Sec. 1.10; Vallis' 1.1-1.3 and Ch.2 do equations of motion analogous to Gill Ch. 4 but we won't get to all of this material for several more lectures.

It would be good to review Lectures 1,2,3 from the fall Fluids course, which are very similar to the 2010 version linked below. The Fluid Dynamics website with course material from 2011 is posted here and the website from the 2014 course just completed should still be on Canvas. But it's handy to have a single .pdf file of the lectures which is linked below.

Chap. 1 of Kundu & Cohen's text has similar material to the above sections of Gill and Vallis.

Chap. 2 of Kundu & Cohen is a review of vector calculus and basic tensor notation useful in FD and GFD. Of particular interest are the divergence theorem and Stokes' theorem, and vector/gradient identities like those in Prof. Bretherton's Fall Q. Fluid Dynamics course: Useful math identities (vectors and differentiation). These can be derived using tensor notation.

- Matlab m-file for 1D, 1 layer geostrophic adjustment from Holton & Hakim Ch.7.
- Week 4 Jan 27, 29 lecture notes
- Week 3 Jan 21-23 lecture notes
- Week 2 Jan 14,16 lecture notes
- Week 1 Jan 6,8 lecture notes (with one typo corrected on 11 Jan)
- Week 1 slides

- Bretherton lectures: Fluid Dynamics, Fall 2010 AS505/OC511.
- Fall Quarter 2014 Fluid Dynamics labs: write-ups with discussion of theory

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

**Lab 1: thermal convection, heat engines****Lab 2: Coriolis-I**: circulation on the rotating Earth.**Lab 3: Coriolis-II**: geostrophically balanced flows.**Fall Quarter 2014 Fluid Dynamics labs**: write-ups with discussion of theory

- A note on Problem Set 2
- Problem set #2. out: 23 Jan, back: 30 Jan.
- Writing notes #2. out 20 Jan., back 22 Jan. The topic is Coriolis effects, and geostrophic balance. Again, two sides of one sheet of paper (or electronic equivalent). Your resources are Gill (and Vallis) texts, the posted lecture notes and GFD lab notes which are quite extensive, and the lectures and classroom exercises themselves. More than repeating equations from the texts, it would be good to include (related to those equations) questions, impressions, applications to real flows and even something you learned or wondered about in a GFD lab experiment. This week's lab (21 Jan.) will be about geostrophic balance and how it is established as flows develop from an initial state. No stratification effects yet.
- Problem set #1. out: 13 Jan, back: 20 Jan.
- Writing notes #1. out: 6 Jan, back Thursday 8 Jan. Write on two sides of a piece of paper notes about the topics from thermodynamics, as seen in Gill's text and lectures. Include questions you have, impressions, possibly an application to an atmosphere/ocean flow (e.g., thermal convection as seen in lab #1).

The class grades will be calculated from:

problem sets and class exercises - 50%

mid-term quiz - 20%

final exam - 30%

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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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AS505/OC511

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