6th Class
Zonal Mean Flow Instabilities
I) Barotropic Instability
Our first analysis of unstable flows will be done for a zonal flow U(y) only a function of the latitude, is called the "pure barotropic" case. In general, when variations of height can be neglected the flow is barotropic.
The solutions that you will analyze are the time evolution (about 7 days) of a zonal flow
U(Y)=U0*Tanh((Yo-Y)/delt), where U0=10m/s Yo=45N and delt=2.5 degrees
The domain is in cartesian coordinates, extends from 30N to 60N in the y direction and different extensions in the x direction, is in an f-plane (f=f0) and has a constant density. Has 129 points in x(i), 99 in y(j) and only 5 levels in z (k). The number of records (l) is about 18. The rest of the parameters are in zeta_setup
The solutions for 5 different wavelengths can be found in /archive/io/ZETAH_netcdf_histories,
BARO_2D001.b1.e10000.nc L=60 degrees longitude
BARO_2D002.b1.e10000.nc L=40 degrees longitude
BARO_2D003.b1.e10000.nc L=70 degrees longitude
BARO_2D004.b1.e10800.nc L=50 degrees longitude
BARO_2D005.b1.e10800.nc L=80 degrees longitude
A) Calculate the growth rate as a function of wavenumber and estimate the maximum growth rate for this flow.
NOTE: The growth rate can be calculated from the growth of eddy kinetic energy
eke={(uu-Xave(uu))^2+vv^2}. A plot of log(eke) vs time will help you estimate the growth rate. { } is the area average
BARO_2D006.b1.e10801.nc L=? degrees longitude
is the history file for the most unstable wave.
B) For the maximum unstable wave calculate the zonal mean flow for the initial time and final time and interpret the differences of these zonal flows.
C) Graph the perturbation stream function (epb(t=33)-epb(t=0)) and describe its circulation
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It will be useful for you to see the time animation of at least one of the solutions.
You can animate in grads by setting the time "set t 1 33" and then displaying the field. A very intersting field to see is vv or epb-epb(t=1). The alternative is to use NCVIEW, NCVIEW is a nice tool to see animations of netcdf files.
To install ncview in your workstation follow the guidelines:
First, make sure you have the correct X-resources for ncview.
Most of the visualizations available can be found at www.gfdl.noaa.gov/~jps/GFDL_VG_2DViz.html
follow the suggestions on the visualization
you can then edit resources
to personalize the look of ncview
Next, create yourself an alias for ncview:
alias ncview '/home/jps/pub/netcdf/util/bin/ncview
-extrainfo -minmax med -private'
Startup ncview by entering :
ncview [nc_file]