Surely you have seen a person exhaling the smoke of a cigarette, cigar or pipe, forming a small but persistent ring rising up in the air. Scaled up and cleaned from the toxicity of the tobacco smoke, the Vortex Cannon shoots thick rings of foggy air which travels metres in an instance, leading to surprise and tousled hair.
One can describe the stream profile at the hole as follows: in the centre of the opening, the molecules of the air move outwards fast. Closer to the edge of the opening the movement is slower, and the molecules in direct contact with the barrel are static. This causes the smoke ring to rotate. As it moves away from the barrel the faster particles from the inside of the barrel circulate around the vortex. The ring remains stable until it reaches its destination or vanishes for the eyes as the smoke gets increasingly thinner. The conservation of angular momentum, which is carried by the ring, lets the force you put in – by hitting the back of the barrel – travel through the air. All this is made observable by nebulising the air.