Vortex Modeling

[Robert Edmonds]

After building my density current model (see: http://stormtrack.org/forum/showthread.php?t=22480&highlight=density+current). I came across point vortex modeling techniques. While I briefly posted about it here before. I recently improved the model. It now uses a higher accuracy finite differencing scheme, and also can take advantage of multi-threading. I ran the model with two 'rings' of vorticity, using 1000 vorticies. While I've seen others do this better this was my attempt over the weekend. I had planed to eventually get this running on a faster computer, so that I could run with tens of thousands of vortecies, however I'm finding the computation time greatly increases (i.e. > N^3).

What's neat about it, is the rings quickly break down because of perturbations, and develop multiple vorticies.


(More red = more vorticity: also this is 2d so vorticity vector is out of the monitor)

Not sure where I am going to go from here... there are some averaging schemes that can fix some of the computation issues. Those take time to build, so I may leave at this for now. There are some tricks I learned with an N-body scheme I used once, so I may be able to adapt it to this, but I need to do a little bit of research. Basically what's bogging down the simulation are the close interacting vorticies.

 

[Robert Edmonds]

I was able to get access to a big computer at the department I work at. The computer has 64 gigs of ram and 16 CPUs I believe. I'm presently running a 10,000 point vortex simulation. To ensure the time stepping didn't get bogged down, I needed to add a sort of 'force/velocity softening' term, that I've used in N-body problems. I have run, and will continue to do, some checks to ensure the results are reasonable. Here is a 'snap shot' of the simulation that will be done in ~2 weeks (that's how long it will take to process).

 

[Robert Edmonds]

Over the weekend made an isolated vortex line model (I need to get a life since this was sort of for fun). I made several runs using different boundary conditions. I can basically make an infinite string, and a loop (shown here). Uses a very different set of equations than for most fluid models, hence the interest.

The line isn't exactly what you would think of when lines of vorticity get carried with the (barotropic) fluid. Instead, the line represents where vorticity is concentrated.


The vortex ring is moving down, but the frame of reference moves with ring. Also, as appropriately the lines don't cross, which is sort of neat since the part of the ring that is close to intersecting doesn't really know (in the calculations) how close the lines are from touching.

As always I welcome questions and comments.