Similarity considerations for non-Boussinesq plumes in an unstratified environment

We develop herein the similarity form of a non-Boussinesq gaseous plume. This is done by obtaining the equation for the conservation of enthalpy flux, and using it and the continuity equation to demonstrate that the flux of density deficiency is conserved, and not the flux of buoyancy as is the case for Boussinesq plumes. We then use this conservation relation to describe the form of the similarity solution in the non-Boussinesq case. The similarity solution is then used to derive the theoretical form of the entrainment velocity across the plume edge, which is seen to be in agreement with the 'modified entrainment assumption' suggested empirically from experiments by Ricou & Spalding (1961).