Entrainment in buoyant jets and fountains revisited

Using a characteristic constant buoyant jet width parameter Cp proposed by List and Imberger [ASCE J Hydraul Div 99(9):1461-1474, 1973], analytical solutions of fully developed Boussinesq round vertical buoyant jets (forced plumes) in a homogeneous, motionless ambient fluid, have been derived using the mass, momentum and buoyancy flux equations of motion. The normalized momentum and volume fluxes are functions of the characteristic jet width parameter and the normalized distance from the source, and congruent to earlier experiments. An equation of the local buoyant jet entrainment coefficient as a function of the Richardson number is derived and its asymptotic values for pure (momentum) jets and simple (buoyancy driven) plumes compare well to laboratory measurements. The entrainment coefficient is a function of Cp and the local Richardson number. It can take values that are lower than the entrainment coefficient of pure, momentum jets, in the case of negatively buoyant jets. Application of the derived entrainment coefficient function to positively and negatively buoyant jets (fountains) can produce results that compare well with laboratory experiments.