Entrainment in plane turbulent pure plumes

Turbulent jets and plumes are commonly encountered in industrial and natural environments; they are, for example, key processes during explosive eruptions. They have been the objects of seminal works on turbulent free shear flows. Their dynamics is often described with the concept of the so-called entrainment coefficient, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\alpha $ , which quantifies entrainment of ambient fluid into the turbulent flow. This key parameter is well characterized for axisymmetric jets and plumes, but data are scarcer for turbulent planar plumes and jets. The data tend to show that the Gaussian entrainment coefficient in plane pure plumes is about twice the value for plane pure jets. In order to confirm and to explain this difference, we develop a model of entrainment in turbulent plane jets and plumes taking into account the effect of buoyancy on entrainment, as a function of the shape of the velocity, buoyancy and turbulent shear stress profiles. We perform new experiments to better characterize the rate of entrainment in plane pure plumes and to constrain the values of the model parameters. Comparison between theory and experiments shows that the enhancement of entrainment in plane turbulent pure plumes relative to plane turbulent pure jets is well explained by the contribution of buoyancy.