A really nice intro is this classic paper on numerical integration of the equation for barotropic vorticity:<p><a href="http:&#x2F;&#x2F;mathsci.ucd.ie&#x2F;~plynch&#x2F;eniac&#x2F;CFvN-1950.pdf" rel="nofollow">http:&#x2F;&#x2F;mathsci.ucd.ie&#x2F;~plynch&#x2F;eniac&#x2F;CFvN-1950.pdf</a><p>It&#x27;s something you can solve in a few lines of python and run with minimal compute resources. A nice thing to try is to feed in some data from somewhere like below and watch what happens as you integrate it forwards in time.<p><a href="http:&#x2F;&#x2F;www.esrl.noaa.gov&#x2F;psd&#x2F;data&#x2F;gridded&#x2F;data.ncep.reanalysis.html" rel="nofollow">http:&#x2F;&#x2F;www.esrl.noaa.gov&#x2F;psd&#x2F;data&#x2F;gridded&#x2F;data.ncep.reanalys...</a>