In my professional life I spend a lot of time thinking about vortices in fluids; the drag they induce and the noise they create. They are common in every-day fluid flows and yet can be quite beautiful.
In their beauty and the compelling way they seem to represent order springing from chaos, there is a trap: the unschooled or unwary can see them as either mystical or unexplained by science.
They are, of course, neither; they are entirely natural and well understood phenomena.
Technically, a vortex is fluid spinning around a centre (or core) with closed streamlines. There are two bounding cases: free (rotational) and forced (irrotational). In the former tangential velocity varies inversely with the distance from the centre. In the latter the fluid rotates like a solid body.