Here you see the good folks on QI shooting smoke rings across the room. Why does a donut-shaped cloud come out of a circular opening? Why are smokers able to blow smoke rings, even when they're not Gandalf? It's all about the physics of vortex cannons!
You can make a vortex cannon without any great effort. Grab a box or an oatmeal container. On one side cut a circular hole, less than half the radius of the container. On the other side, cut the end clean off and replace it with cling film that's sealed over the container. Plunk the cling film and boom - you've got a vortex cannon. To see anything interesting, of course, you need a smoke machine, which is why we love the BBC so much.
But if you've noticed, although the holes in the cannons are round they shoot smoke rings. The technical term for a donut shape is "torus," and one of these floating rings is called a toroidal vortex. Air (and smoke) are spinning from the inside of the donut to the outside, like rotating beads on a bracelet. This spin is what keeps the torus together as it moves across the room.
A good deal of the air shot by a cannon does blast straight out of the cannons as they fire. But some of the smoke gets dragged out and back by the edge of the ring out of which it was fired, and by contact with the outside air. It meets the air around it and starts curling backwards, looking like the edge of a mushroom cloud. The drag from the air and rim on one side, and the push from the smoke on the other, gets that patch of smoke to begin spinning, creating a vortex. The smoke still maintains some forward momentum, and so the ring travels across the room. If it weren't spinning, the friction of the air around it would cause it to break apart. Because it is spinning, it's moving faster than the air around it.
The Bernoulli Principle states that as air picks up speed, air pressure drops. This means that the air in the ring is at a lower pressure than the air on all sides around it. This causes the air around it to push inwards, like a giant mold, keeping the torus together as it moves. And so, smoke rings jet around, amusing and entertaining all.