Turbulent buoyant convection from a source in a confined region

Abstract

An extension of the model first proposed by Baines & Turner (1969) is derived with careful attention to the conditions required for its application. The most important of these are that the Prandtl number ν/kis of order unity or greater, the ratio of the lengthLto depthHof the region is greater than about 1·2 for the two-dimensional region considered andRis so large thatR[gsim ]L/HandR[Gt ] 1/α. The characteristic group\[ R\equiv \alpha^{\frac{2}{3}}F_0^{\frac{1}{3}}H/\nu. \]R2is a Grashof number based on the source strengthF0of the buoyant convection which is modelled using turbulent plume theory and the entrainment constant α, the ratio of inflow velocity across the edge of the plume to mean local plume velocity. The conditions onRensure that the source of buoyant convection is the dominant transportive mechanism in the region and the restrictions on the aspect ratio ensure that there is clear separation between the passive motions in the bulk of the region and the intense highly confined buoyant convection.The manner in which the convective fluid recirculates to become part of the passive interior is studied and shown to be controlled by the same dynamics as fluid intrusion into a stably stratified environment.Several new solutions are obtained, including cases of steady conditions involving only one source.