Entrainment in two coalescing axisymmetric turbulent plumes
A model of the total volume ﬂux and entrainment occurring in two coalescing axisym-metric turbulent plumes is developed and compared to laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In Region 1, where the plumes are separate, the entrainment in each plume is unaﬀected by the other plume, although the two plumes are drawn together due to the entrainment of ambient ﬂuid between them. In Region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In Region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We ﬁnd that the total volume ﬂux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume ﬂuxes at the touching and merging heights. Finally, we deﬁne an ‘eﬀective’ entrainment constant, αef f, as the value of α needed to obtain the same total volume ﬂux in two independent plumes as that occurring in two coalescing plumes. The deﬁnition of αef f allows us to ﬁnd a single expression for the development of the total volume ﬂux in the three diﬀerent dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume ﬂux in the two coalescing plumes as they evolve through the three regions.