Unique Superposition Solution of Multiple Plane or Round Buoyant Jets for Tracer and Buoyancy Fluxes

Abstract

The present paper proves the uniqueness of the superposition solution regarding tracer or buoyancy for parallel multiple (plane or round) turbulent buoyant jets with positive buoyancy in general, which are discharged vertically upwards into a still environment from sources of relatively short spacing. The multiple plane buoyant jets are of infinite length, whereas the multiple round buoyant jets may form groups of any arrangement shape. The proof is based on the observation that the partial differential equation of tracer or buoyancy conservation becomes linear with respect to the mean tracer or buoyancy fluxes of single plane or round turbulent buoyant jets, which simultaneously satisfy the aforementioned equation. Alternatively, the validity of similar assumptions to the Reichardt’s hypothesis, for either plane or round turbulent buoyant jets, has been verified. Findings denote that the solution of a group of interacting buoyant jets with respect to the tracer or buoyancy fluxes can be uniquely obtained by superimposing the particular solutions corresponding to each single buoyant jet of the group. In addition, the superposition method is suitably applied to predict the profiles of the tracer or buoyancy flux above a finite two-dimensional or three-dimensional source.