Simple modelling will enable many properties of fully developed, turbulent plumes to be investigated. Many of the classic scaling arguments were developed in a combined analytic and laboratory study described in an influential paper by Bruce Morton, G.I. Taylor and Stewart Turner and this and subsequent work is described in the popular monograph of Stewart Turner.
# 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).
# The distribution of density and velocity across the plume are modelled either with simple Gaussian distributions or else are taken as uniform across the plume (the so-called top hat model).
# The rate of entrainment into the plume is proportional to the local velocity.  Though initially thought to be a constant, recent work has shown that the entrainment coefficient varies with the local Richardson number.  Typical values for the entrainment coefficient are of about 0.08 for vertical jets and 0.12 for vertical, buoyant plumes whilst for bent-over plumes, the entrainment coefficient is about 0.6.
# Conservation equations for mass (including entrainment), and momentum and buoyancy fluxes are sufficient for a complete description of the flow in many cases. For a simple rising plume these equations predict that the plume will widen at a constant half-angle of about 6 to 15 degrees.
The value of the entrainment coefficient is the key parameter in simple plume models. Research continues into assessing how the entrainment coefficient is affected by, for example, the geometry of a plume, suspended particles within a plume, and background rotation.