MIXING BY A TURBULENT PLUME IN A CONFINED STRATIFIED REGION

An experimental and theoretical study of the mixing produced by a plum e rising in a confined stratified environment is presented. As a resul t of the pre-existing stable stratification, the plume penetrates only part way into the region; at an intermediate level it intrudes latera lly forming a horizontal layer. As time evolves, this layer of mixed f luid is observed to increase in thickness. The bottom front advects do wnward in a way analogous to the first front in the filling box of Bai nes & Turner (1969), while the lateral spreading of the plume occurs a t an ever-increasing level and an ascending top front results. We deve lop a model of this stratified filling box; the model predicts the rat e at which the two fronts advance into the environment. It is found th at stratification in the environment, when smooth, has no significant influence on the dynamics of the descending front. We show that the ra te of rise of the ascending front is determined by the turbulent mixin g occurring at the spreading level. Entrainment of environmental fluid from above into the overshooting plume is significant; as a result, a density interface develops at this level. Asymptotically, the system reaches a state in which a bottom convecting layer, with an almost hom ogeneous density, deepens in a stratified background. The model propos ed for this large-time behaviour is based on the simple energetic form ulation that a constant fraction of the kinetic energy supplied by the plume, for mixing across the interface, is converted into potential e nergy of the convective layer. Our experimental results suggest an eff iciency of approximately 50 % for this conversion. We discuss our resu lts in the light of previous studies on turbulent penetrative convecti on and conclude that the theory developed should be valid for an inter mediate range of values of the Richardson number characterizing the dy namic conditions at the interface. The model is applied quantitatively to the process of cooling of a room wherein stratification is relevan t. The geological problem of replenishment of a magma chamber by a lig ht input of magma is also analysed.