The flow in and around air-bubble plumes

(1) A short review is given of some of the important publications on air-bubble plumes. Two main ways of modelling, using either the entrainment assumption, or the energy balance principle, are presented and briefly compared. (2) Focusing attention on the entrainment coefficient α(z), we show how useful information about this coefficient can be found, for a plane plume, from the characteristics of the external flow (the “return flow”). (3) A theory is presented for the external flow far outside a plane plume, at horizontal distances x⩾3D, D being the water depth. (4) A similar theory is presented for the surface flow close to the plume (both axisymmetric and plane cases covered). Our theory replaces the physically non-permissible assumption about conservation of momentum around the turning region, used in earlier approaches, with an energy condition in which turbulent dissipation is included. Comparisons of the theories with experiments reported in the literature show reasonable agreement.