I'm on a 3 minute break, and don't think I can be certain of my answer in 3 minutes. Some thoughts that mig
ht be considered for a solution:
gyroscopic precession
pressure in water increases with depth
Feynman sprinkler
If there is a slight amount of movement initially, then could the treads on any tire act like the dimples of a golf ball, causing a difference in pressure depending on the direction of spin?
Is this wheel neutrally buoyant though? My other canned response is, "it'll go up. Wheels with inflated tires float." At least, I think they do.