updated 7i2004 
ATM S 509/OCEAN 512 SLN:
1548 (ATM), 6180 (OCN)
MWF 10:30-11:20, Lectures in ATG 310
Th 2:30-3.20 Lab demonstrations in OSB 107
[OSB is Ocean Sciences Building, newly built, on Boat St at 15th Ave NE]
Geophysical Fluid Dynamics - I - Winter 2004
Instructor:
|
Professor P.B.Rhines
Ocean Sciences Building 319
tel: 543-0593
rhines@washington.edu
office hours: MW, 2:30-3:30pm and by appointment |
Teaching Assistant:
|
Daniel Kirshbaum
Atmos. Sci. - Geophys. Building 620
tel: 685-9305
dank@atmos.washington.edu
office hours: MWF 11:30am-12:20pm and by appointment |
GFD-1 webpage from 2001, with lots of worked out problems/quizzes here.
NEWS NOTES,
12 iii 2004
atmospheric data (matlab file for 2002 dynamic height fields) here. Sample plot instructions (as an m-file) here.
ETOPO2 topography dataset here (this is 2
minute resolution..2
nautical mile or ~4 km resolution); as a .mat file;
A subset of the IBCAO new higher resolution topography here. This is just the subpolar Atlantic I
think. A figure showing the whole IBCAO domain is here, and a zoomed in region of the
west Greenland coast is here.
12 iii 2004
Ekman layer notes are posted below.
11 iii 2004
Solutions to PS 5 are posted below.
Today problem solving session at 2.30 in 310 classroom.
***By request of students, exam will be at 10.30-12.20 Monday
March 15
in room 610 of Atmospheric Sciences, up 3 floors above the
classroom.*** The exam will be open book, open notes.
5 iii 2004
Reading on Ekman layers and spin-up is listed below
2 iii 2004
Posted below are some notes on math. for GFD: pde's and wave
mathematics. This is optional material from today's review class,
and I have added a few things to the paper version handed out.
1 iii 2004
TAKEHOME QUIZ HANDED OUT THIS THURSDAY AT GFD LAB 2.30 pm
RETURN BY 3.00 PM FRIDAY 5 MARCH
Math review (optional)
tomorrow Tuesday 2 iii 04 at 2.00 pm in 310.
The lecture notes on
stratified rotating flow are posted below with some sign corrections, and
with an added section on the effect of the upper boundary...revisions
mostly in purple.
Interesting televideo climate lecture this
Weds. 3 iii 04 at 9.00 am, T-239 Health Sciences; see notice in Atmos
Sciences
elevator. Dr. David Beerling speaking from Univ. of Sheffield England on
'Putting ecosystem chemistyr into models of past global change." This is
at UW-TV studios in T-wing of Health Sciences, which is near the ground
floor outdoor entrance to H.S. across from the South Campus Center.
27 ii 2004
Notes on the Boussinesq approximation posted
below. TAKEHOME QUIZ given out at lab next Thursday, March 4, due back
Friday March 5 by 3.00 pm.
25 ii 2004
M-file for Matlab plots of flow and pressure available below, for
both the circular cylinder (full depth) and circular mountain. 23 ii 2004
Posted below are images from the PIV (particle imaging velocity) data
from the flow-over-a-mountain experiment in the lab, analyzed by David
Peterson. Pairs of images of floating particles are compared by computer,
giving estimated velocity vectors.
Posted below is problem set 5 with some typos corrected and a few
added explanatory notes.
Also below are solutions to PS4.
18 ii 2004
Some new downloads are below: the m-file to make Matlab plot
of pressure/streamfunction in 2D flow round a cylinder, and the
numerical model solving the 1-layer wind-driven flow in a zonal
channel, or geostrophic adjustment in the channel.
Baroclinic geostrophic adjustment lab images and text are posted.
Readings in Gill are sections 7.8-7.12 for vorticity dynamics and APE.
Note
also good sections on thermodynamic and mechanical energy, 4.4,4.6,4.7
Soon will have a handout on the Boussinesq approximation
8 ii 2004
Solutions to problem set 3 are posted below.A new set of slides (#3) is
posted.
This week's lab (Feb 12
Thursday 2.30) will deal with stratified geostrophic flow, thermal wind,
and geostrophic adjustment. Lectures will continue with vertical
structure, stratification effects and introduce vorticity and potential
vorticity. A brief discussion of thermodynamics will be given. Readings
in Gill will catch up with vertical structure,
thermodynamics and vorticity.
2 ii 2003
Reading assignments in Gill are posted below. The mechanical energy
equation sections are given; note that the first time this appears is in
Sec. 4.6, although the single-layer model is better discussed in the other
sections listed below.
Severinghaus lecture: There is a teleconference/lecture originating at
Univ. California San Diego, 9.00 am on Weds. 4 Feb just before class on A
View of Abrupt Climate Change from Gases Trapped in Glacial Ice: T-239
Health Sciences (which is UW-TV studios). It is part of a WUN (World
Universities Network) series (posted in Atmos Sciences elevator). The WUN
sponsors grad student exchanges between UK and USA as well as other
countries.
Problem Set 3: a revision correcting minor typos is posted below. It
will be due Thursday, 5 Feb
A Take-home quiz will be handed out at the lab on
Thursday, 5 Feb, due back at 10.30 Friday 6 Feb in class.
Notes on Problem 4 of PS 2 are posted below.
All 3 lab writeups are now posted, as are 2 sets
of lecture slides.
The web site from the 2001 GFD-1 course is available with many
solved homework problems, lab images, etc.
..here.
Course Description
Dynamics of rotating stratified fluid flow in the atmosphere/ocean and
laboratory analogues. Equations of state, compressibility, Boussinesq
approximation. Geostrophic balance, Rossby number. Poincare, Kelvin,
Rossby waves, geostrophic adjustment. Ekman layers, spin-up.
Continuously stratified dynamics: inertia gravity waves, potential
vorticity, quasigeostrophy.
Animations:
Excellent loops at www.atmos.washington.edu especially (both models, global assimilated observations and local models for NW USA;
also, www.weather.unisys.com.
Prerequisites
A course in basic fluid mechanics, particularly Ocean 511A, Atmos Sci
505A, Amath 505a
Textbook
Gill, A.E. Atmosphere-Ocean Dynamics. Academic Press
Week 1-2 Chapters 1; 2; 3.1, 3.5-3.7; 4.1-4.5
Weeks 3-5 Chapter sections:
7.1-7.2, 7.4-7.6 (effects of rotation);
8.1-8.3 (rotating, hydrostatic waves);
10.4-10.5 (Kelvin waves)
The mechanical energy equation is discussed in Gill sections 4.6,
5.7, 8.3
Weeks 6-7
7.7-7.12 (thermal wind, vorticity, APE)
4.4, 4.6,4.7 (thermodynamic and mechanical energy)
Weeks 9-10
Lecture notes on quasi-geostrophic PV (available below)
Gill 9.1-9.6, 9.12 (Ekman layers and spin-up)
Background/alternative texts:
Holton,J. Introduction to Dynamical Meteorology, Academic Press
Pedlosky, J. Geophysical Fluid Dynamics. Springer Verlag
Salmon, R. Lectures in Geophysical Fluid Dynamics. Oxford
University Press
D.J. Acheson, Elementary Fluid Dynamics. Oxford University
Press.
P.K. Kundu, Fluid Mechanics. Academic Press.
For vorticity dynamics:
Lighthill, M.J., An Informal Introduction to Theoretical Fluid
Mechanic, Oxford Univ. Press
Batchelor, G.K., An Introduction to Fluid Dynamics
, Cambridge Univ. Press
See Outline-2004 for more references
Class Notes
Please take notes. We will try to help out by posting as much
lecture material as possible on this page.
Lecture Notes and Supplemental Reading
Labs
Visit the GFD lab
website and a poster showing
some of our teaching, term projects, and research in the lab. We teach
lab projects courses of various kinds; on the poster site, click on the
'1997 Undergraduate Projects Course' then on 'Sediment mobilization in
the Surf Zone' an example of undergraduate work. Click on 'Graduate GFD
Projects Course' too.!
Schedule and Homework
Lee cyclogenesis: shedding a vortex off a mountain
.
Below are 4 images from computer analyzed images from the lab demo on
vortex stretching. The 'dye images' can be found on the Coriolis lab
image clicker in the matrix above, or on the Feb 2004 page of the UW
Office of Research calendar.
The mountain is at top center, and an anticyclone forms above it and
is trapped there. A cyclone forms in the fluid pushed off the mountaintop
and swept downstream. The color indicates speed. [The upper two
images are actually a different experiment than the lower two, the
difference being that the mean zonal flow persists in the upper
images, while we 'switch it off' by twiddling the rotating table
control, in the lower two. Analysis by David Peterson.
The theoretical steady solution depends on Rossby number, but
sample images of the pressure, or eta, or streamfunction are below.
The titles should read "Ro H/d = 0.3 and ... = 1".
Below, pressure field or free-surface height field for 2-dimensional
flow (into the screen) past a circular
cylinder, with Coriolis effects. Left: moderate Rossby number, right:
infinite Rossby number (no rotation effects). Beneath are two more
figures showing contours of streamfunction and pressure for moderate and
low Rossby number.
Even at very low Rossby
number, when the
isobars nearly coincide with streamlines, there are essential dynamic
pressure variations along streamlines. The high pressures are at the
forward
and aft stagnation points, with low pressure on the two sides where the
velocity is greatest. To this non-rotating pressure field is added a
function of psi, the streamfunction which gives the high pressure to the
right and low pressure to the left. In the unusual case of purely
2-dimensional flow, the flow itself (the streamline pattern) is not
affected by rotation, although the pressure is.
Modelled Kelvin waves traveling eastward along the equator in the
Pacific; note how they turn poleward after hitting mountain barriers,
particularly the Andes at 80W longitude...the atmosphere has walls!
Fields are outgoing longwave radiation and sealevel pressure, 40 hPa
contour interval; these are launched as part of the Madden-Julian
Oscillation. . From Hadley Center GCM, Matthews et al., Quart J. Royal
Met Soc 1999. Wave speed is about 55 m/sec.
click on the Rossby wave
Grades
The following is the revised plan for 2004.
Your course grade will be based on problem-set homework, takehome quizzes and exams. There will
be problem sets due one week after being handed out. These will be
worth 40% of your grade. Problem sets can be solved in groups, with collaboration.
Please note that it is essential for your learning that you wrestle with these problems, even if
someone else has produced an analysis.
There will be two take-home quizzes which are to be solved individually without any collaboration, and will
contribute 30% of your grade.
The final exam will contribute 30% of your grade.
While the lectures define the core material for the course, some
material from reading assignments will be included in exams; we will
specify how much detail this involves. Lab demonstrations are also a
part of the required material, and ideas from these may appear on
problem sets, quizzes and exams.
Consulation hours for Kirshbaum and Rhines will be established: please
see us when the lectures or homework do not make sense to you.
Above: the shape of the Earth's geopotential surfaces
Hurricane Bonnie. Note cloud streets over Florida and Cuba indicating
rotary winds. If Ekman convergence causes rising motion at a
low-pressure center, why is there usually (unfortunately not visible
here) a clear eye in a hurricane?
Above, unstably growing eddies in Weddell Sea, marked by ice (320x260km)
Isopycnal model simulation of N. Atlantic circulation surface temp
(R.Bleck, Micom)
