Stratification and convection produced by multiple turbulent plumes

Abstract

A study of convection in a finite box is presented, in which two or more buoyancy sources produce well-separated, turbulent plumes. In the “filling-box” problem, where turbulent plumes “fill” a finite box, the source with the largest buoyancy flux produces the plume that descends to the bottom to give rise to the “bottom waters”. Each of the sources having smaller buoyancy fluxes produces water that spreads at an intermediate depth. We study the “filling-box” convection from two or more well-separated turbulent plumes and present numerical solutions and for large times, analytical approximations. These show that the spreading depth of a weaker plume is dependent on the 2/3 power of the ratio of its buoyancy flux to the flux of the strongest plume, a result which is verified by experiments. The experiments also show that the circulation pattern formed consists of a number of counterflowing shear layers. This pattern is primarily forced by the bottom outflow from the source with the largest buoyancy flux, but is modified by the volume flux injected at shallower depths by the weaker plume. The pattern is supported by the stable density stratification produced collectively by all the sources. Because the horizontal velocities in the shear layers dominate over all other horizontal motions, they influence the spreading of each intermediate-depth outflow. The results may be of significance to the thermohaline circulation of the oceans, where there are a number of intermediate and deep water sources.