Mathematical Description for Steam Rising from a Cup !enter image description here I was staring at a cup of coffee I have on the desk just now. The light shines through the water vapor as they rise from the cup. The shape of the steam is not completely random, as it drift from hot area to cold area according to the second law of thermodynamics. If you whiff your hand over, the steam swirls with a distinct center of rotation. How would one go about describing the shape and characteristics of the steam as it rises from a hot cup of water? What branches of math would be involved in creating such a model?

Computer graphics has been simulating this using fluids dynamics for some time now. See for instance Vortex Fluid for Gaseous Phenomena and Cuppa Coffee and The Lonely Cigarette.