A Closure for the Virtual Origin of Turbulent Plumes

Abstract

AbstractAn isolated source of surface buoyancy, be it a campfire or burning city, gives rise to a turbulent plume. Well above the surface, the plume properties asymptote to the well-known solutions of Morton, Taylor, and Turner (MTT), but a closure is still lacking for the virtual origin. A closure for the virtual origin is sought here in the case of a turbulent plume sustained by a circular source of surface buoyancy in an unstratified and unsheared fluid. In the high Reynolds number limit, it is argued that all such plumes asymptote to a single solution. Direct numerical simulation (DNS) of this solution exhibits a virtual origin located a distance below the surface equal to 1.1 times the radius of the buoyancy source. This solution is compared to the previously used assumption that the MTT plume is fully spun-up at the surface, and that assumption is found to give buoyancies that are off by an order of magnitude. With regards to the citywide firestorm triggered by the nuclear attack on Hiroshima, it is found that the spun-up-at-surface MTT solution would have trapped radioactive soot within about a hundred meters of the surface, whereas the DNS solution presented here corroborates observations of the plume reaching well into the troposphere.