VORTEX FORMATION BY SUCCESSIVE THERMALS: A NUMERICAL SIMULATION

Abstract

The purpose of this research is to investigate, by means of numerical simulation experiments, the complex interactions between consecutive toroidally circulating buoyant elements (thermals) when these occur in either rotating or nonrotating environments. The study includes both the vortex formation process and the effect that this process has on the properties of the one or more buoyant elements involved in the interaction. A numerical model of a self-developing thermal of the Ogura type was modified to include tangential accelerations and a provision for injecting a second thermal into the field of a previous one. Computer outputs are obtained at several times during the evolution of both solitary thermals and two types of successive thermals, released at intervals of 2 and 7 min. These were also performed for three different magnitudes of pre-existing vorticity, comparable to magnitudes measured in the vicinity of thunderstorms. The results of the complex interactions are illustrated in the patterns of isotherms, stream functions, and velocity isotachs. A thermal is accelerated in circulation and velocity of rise upon encountering the wake of a previous thermal, and velocity enhancements can be quite spectacular. A rotation field causes both solitary and successive thermals to surrender part of their kinetic energy to vortex formation, but lateral confinement of the thermal slows the mixing and reduces the heat loss. The first effect tends to suppress the vertical momentum of the thermal, and the second one tends to enhance it. Nevertheless, all but one of the solitary and successive thermals investigated were suppressed by the vortex formation interaction; this one, a second thermal with a 7-min interval, appears to represent an optimum combination of buoyancy and ambient vorticity, since it forms a more intense vortex and simultaneously maintains the strongest vertical velocity for one particular magnitude of ambient vorticity. When the rotation rate initially is very large, on the other hand, a solitary thermal is ?dominated? by the rotation field, and neither forms a strong vortex nor develops the usual characteristics of a vigorous thermal. The results show several features of the numerical simulation to be in agreement with solitary and successive thermals simulated in the laboratory. Some possible recognition features are suggested for the detection of situations where strong interactions occur between a buoyant element and the ambient vorticity field. Some of the results must be applicable to atmospheric convection. The computations relating to vortex formation must be considered relevant to tornadoes, despite the shallow depth used for the convection layer.