Good observation, but sometimes you actually want to induce those counter rotating vorticies.
jacksoni I think we spoke about this over email.
Where you are getting air under the car, a bellypan is going to increase downforce, mostly at the front. It can increase rear downforce should there be a diffuser to take advantage of that since you have more attached air under the car. Increased downforce normally results in increased drag, but it doesn't have to. it depends on how you manage the wake in the base pressure behind the car and, as WW pointed out, managing the cross flow between sides and floor too.
The thing to watch for with belly pans (or any underbody ground effect aero stuff) is pitch sensitivity. A highly pitch sensitive car will have large swings in downforce due to relatively small changes in vehicle attitude. That will go from mildly poor handling to "oh crap I'm flying" very quickly. There are methods to mitigate this, most take time in a tunnel, but there could be empirical ways to do this on the salt if you have some patience to make changes and run conservative speeds until you are satisfied with the safety. This is one of those areas of development I would ONLY trust to a moving ground wind tunnel or actual track data. Fixed ground tunnels raise alot of questions here.
Of course if you have an air dam or other blockage device at the front of the car a bellypan will most likely not do much.
