Analytical solutions and virtual origin corrections for forced, pure and lazy turbulent plumes based on a universal entrainment function
Francesco Ciriello, Gary R. Hunt
Abstract
Previous measurements and numerical simulations of buoyant turbulent plumes that develop from area sources provide convincing evidence that entrainment varies locally in response to an imbalance from the asymptotic state of equilibrium, a state referred to as a pure plume. Across the wide spectrum of possible source conditions, that span forced and lazy plume releases, this variation of entrainment has been successfully captured by a single, or universal, description in which the entrainment function solutions of the plume conservation equations. Analytical solutions for the fluxes of volume and specific momentum are first developed. These solutions highlight the deficit in near-field entrainment in forced plumes and enable the general imbalance from the equilibrium state to be predicted via the streamwise variation of the local Richardson number. Focus then turns to the virtual origin due to the practical benefits that a knowledge of this location offers experimentalists (e.g. in comparing measurement with theory) and theoretical modellers (e.g. in incorporating a turbulent plume within a broader modelling framework).