Large-eddy simulation of a buoyant plume in uniform and stably stratified environments

Abstract

We consider large-eddy simulation (LES) of buoyant plumes in uniform and stably stratified environments. We show that in the former case the results agree well with the simple plume model of Morton, Taylor & Turner (Proc. R. Soc. Lond. A, vol. 234, 1956, p. 1). In particular, we calculate an entrainment constant which is consistent with laboratory and field measurements and find no significant difference between the radial spreading rates of vertical velocity and buoyancy. In a stably stratified environment, the LES plume shows better agreement with Morton et al. (1956) below the level at which the buoyancy first vanishes than above this level. Above the level of neutral buoyancy, the LES plume is characterized by an ascending core of negative buoyancy surrounded by a descending annulus of positive buoyancy. We compare the LES data with the model of Bloomfield & Kerr (J. Fluid Mech., vol. 424, 2000, p. 197), which explicitly accounts for these coherent motions. The model exhibits many qualitative aspects of the LES plume and quantitative agreement can be improved by adjusting the downward volume flux relative to the upward volume flux in a manner consistent with the LES plume. This simple adjustment, along with revised values of the entrainment constants, represents the combined effects of an overturning region at the top of the plume (where a fluid element reverses direction), ‘plume-top’ entrainment (whereby the plume entrains ambient fluid above the plume) as well as lateral entrainment and detrainment processes (both external and internal) occurring above the top of the model plume.