Usually, as a plume moves away from its source, it widens because of entrainment of the surrounding fluid at its edges. This usually causes a plume which has initially been 'momentum-dominated' to become 'buoyancy-dominated' (this transition is usually predicted by a dimensionless number called the Richardson number).
A further phenomenon of importance is whether a plume is in laminar flow or turbulent flow. Usually there is a transition from laminar to turbulent as the plume moves away from its source. This phenomenon can be clearly seen in the rising column of smoke from a cigarette.
Another phenomenon which can also be seen clearly in the flow of smoke from a cigarette is that the leading-edge of the flow, or the starting-plume, is quite often approximately in the shape of a ring-vortex (smoke ring).
Plumes are of considerable importance in the dispersion of air pollution. A classic work on the subject of air pollution plumes is that by Gary Briggs.
A thermal plume is one which is generated by gas rising from above heat source. The gas rises because thermal expansion makes warm gas less dense than the surrounding cooler gas.
Quite simple modelling will enable many properties of fully-developed, turbulent plumes to be investigated (see eg ).
For a simple rising plume these equations predict that the plume will widen at a constant half-angle of about 6 to 15 degrees.
A top-hat model of a circular plume entraining in a fluid of the same density is as follows:
The Momentum M of the flow is conserved so that
The mass flux J varies, due to entrainment at the edge of the plume, as
This shows that the mean velocity v falls inversely as the radius rises, and the plume grows at a constant angle dr/dx= k'