In hydrodynamics, a plume is a column of one fluid moving through another. Several effects control the motion of the fluid, including momentum, buoyancy and density difference. When momentum effects are more important than density differences and buoyancy effects the plume is usually described as a jet.

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 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 see in the rising column of smoke from a cigarette.

Another phenomenon which can be seen clearly in cigarette flow is the leading-edge of the flow, or starting-plume, which is often approximately a ring-vortex (smoke ring) (see say Turner, ref. 2)

Plumes are of considerable importance in the spread of pollution. A classic work on the subject is that by Gary Briggs (eg 'Plume Rise Predictions', USAEC, 1969 and ref. 1)

Simple Plume Modelling

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Quite simple modelling will enable many properties of fully developed turbulent plumes to be investigated. 1) It is usually sufficient to assume that the pressure gradient is set by the gradient far from the plume (this approximation is similar to the usual Boussinesq approximation)

2) The distribution of density and velocity across the plume are modelled either with simple Guassian distributions or else are taken as uniform across the plume (the so-called 'top hat' model).

3) Mass entrainment velocity into the plume is given by a simple constant times the local velocity - this constant typically has a value of about 0,08 for jets and 0.12 for buoyant plumes.

4) Conservations equations for mass flux (including entrainment) and momentum flux(allowing for buoyancy) then give sufficient information for many purposes.

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 $\backslash rho$ is as follows:-

The Momentum M of the flow is conserved so that

$A\; \backslash rho\; v\; ^2\; =\; M$ is constant

The mass flux J varies, due to entrainment at the edge of the plume, as

$d\; J/d\; x\; =\; d\; A\; \backslash rho\; v/dx\; =\; k\; r\; \backslash rho\; v$

where k is an entrainment constant, r is the radius of the plume at distance x, and A is its cross-sectional area.

This shows that the mean velocity v falls inversely as the radius rises, and the plume grows at a constant angle dr/dx= k'

Reference

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1. Briggs, Gary A (1975) Plume Rise Predictions, Amer. Met. Soc.

2. Turner, J. S. (1962) The Starting Plume in Neutral Surroundings, J. Fluid Mech. vol 13, pp356-368

THIS IS WORK IN PROGRESS, produced mainly as a reference for the Hemel Hempstead oil fire :-) Google on the key terms (and Briggs) for more (and perhaps more reliable) information in the interim

fluid dynamics