Instructor: |
Professor P.B.Rhines Ocean Sciences Building 319 tel: 543-0593 rhines@washington.edu office hours: MW after class, and by appointment. |
Teaching Assistant: |
Alison Gray (alison@ocean.washington.edu) 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 |
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.
Note that thermal wind balance follows from horizontal geostrophic balance and vertical hydrostatic balance in the MOM conservation equations. Hydrostatic balance is very accurate at large scale (recall the (H/L)^2 parameter). So, testing geostrophic balance is close to testing thermal wind balance: one way to do this involves basic plots of dynamic height contours (in lat-lon maps) and superimposing horizontal velocity vectors on them using the "quiver" command in Matlab. Then line plots along specific longitudes could be made to quantitatively compare Coriolis force and dynamic height gradient, at different vertical levels. This strategy may be easier than the explicit comparision involved in thermal wind balance, but both approaches are valuable.
Another way to test geostrophic balance is to calculate vertical
vorticity ζ =dv/dx - du/dy and divide it by f. THis ratio is a Rossby
number
that will be <<1 for geostrophic flow. Maps of ζ/f are very rich
(we mention this and PV maps in the original problem set). Note the
connection between ζ
and the horizontal Laplacian of the dynamic height or pressure:
.
Also think of Z or pressure as a streamfunction for the geostrophic
velocity: constant Z contours or isobars are nearly streamlines of
the horizontal flow, and their spacing is inversely proportional to
fluid speed, with a scale factor 1/f that varies with latitude.
The Matlab command zeta=curl(lon_m,lat_m,ua',va'); calculates vorticity
from the stored velocity data, and this is the most direct way
to create this Rossby number map (comparing this with the
geostrophic approximation above would be interesting but some work).
In "curl..." you need to adjust latitude and longitude in meters instead
of degrees (that's what lon_m and lat_m mean). ua and va are the u and v
velocities on a single pressure level).
An atmospheric dataset for 2010 has been uploaded here. It is
large..154 Mbytes. Try loading it and making some plots. If the size is
a problem contact me. It is a Matlab file
ncep-data-2010.mat The variables
are dynamic height, u, v, temperature daily, at 17 pressure levels. It
is also posted under Observational Data below. Here is
some description.
WEEK 4 Friday 21 Jan 2011.
Because of AMS meeting next week due date for problem set 2 is
now Friday 28 Jan.
Images from lab 3 (geostrophic flow) with discussion are
posted
below or here.
When 'typos' and other errors are found in lecture notes
and problem sets they will be corrected in the .pdf's posted here, and
listed. Today the following turned up: problem set 2: units of mass
transport (prob 2) are kg/sec not kg m^-3 sec^-1 and cos(ikx -i sigma t)
should read cos(kx -sigma t) in prob. 3. Also in lecture 5/6 notes the
equation just following equation (7) should have a minus sign instead of
plus sign; lecture 7/8 notes have been corrected for an error in the
discussion of long waves with rotation. See reposted
notes for more.
In class today I described the goal of the Google Docs, which are to provide a site for you to describe work with observational data sets relating to gfd dynamics. Specific suggestions will be posted with each data set. While we want this to be relatively unstructured, it is an important part of the course and provides a mechanism for one-on-one interaction with you. Post your results (including figures or links to .pdf's or videos) on your Google Doc.
The Google Doc is also a good place for you to give impressions
about the course material: what in Fultz's movie Rotating flows
made sense or was provocative or interesting? What in lectures or
problems or labs was unclear and could be further explained? What in
your own research area relates to GFD ideas presented? How do you find
Gill as a text?
Wednesday 19 Jan 2011.
Thanksgiving 2010 snowstorm and GFD lab tornado illuminated with laser light-sheet
cat-scan.
There are in addition other fluid dynamics and GFD textbooks and each has its merits:
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,
http://www.atmos.washington.edu/academics/classes/2010Q4/505/ .
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
GFD-1 carries on fairly continuously from Fluid Dynamics, AS505/OC511, Fall 2010. We will revisit
much of that material so keep Prof. Bretherton's notes handy. The course material is still posted here.
You will have a Google Document online, shared with the instructors. In part it is to be a 'journal' It is an important part of the course. We hope to see your developing thoughts about the reading, about the lectures, questions about ideas that are not clear, and discussion of ideas that seem exciting. Figures can be posted there, and we can develop links with the class to stimulate broader discussion.
The GoPost bulletin board is now active. Try to think of GoPost and your Google Doc as companions: we're trying the experiment of 'journals' or diaries with Google Doc (viewable by you and the instructors only), in which you record your daily reading impressions, excitements, frustrations with the GFD material, and perhaps register your own insights, images, web-links that can enhance the experience. We instructors will comment now and then on your journal; in particular in response to questions regarding reading and homework. Then, you might want to transfer a few of your observations to the GoPost board, in hopes of stimulating a discussion (or, just stimulating). We'll be in the background watching and if we have anything useful to say, will do so.
Also we will have the above linked sections (Course description...outline...) filled in soon, and a grading algorithm posted (the journal-keeping exercise will be a part of the course grade; try to keep a running account of impressions from the reading/lectures but don't feel that you must summarize or paraphrase all the material ). -PBR, ARG