The choice of conservation equations for plume models

Abstract

Theories on the behavior of turbulent buoyant plumes generally form three classes: (1) strictly self-similar models valid only in a uniform environment; (2) quasi-similar models based on flux conservation of mass, momentum, and heat; and (3) quasi-similar models based on conservation of momentum, heat, and kinetic energy of mean motion. Few direct comparisons of the various numerical solutions for the different models have been reported; and little attempt has been made to compare the formulation of models (2) and (3) in spite of the fact that such a comparison must form the basis for an understanding of their differences. The following contribution has been stimulated by yet another solution published recently by Fox in this journal, but differs from earlier papers in that it concentrates wholly on a discussion of the equations used in the two quasi-similarity approaches. The relationship between the field and gross-flux forms of the equations of motion is considered. In particular, it is shown that the use of the flux equations for vertical momentum and kinetic energy is not equivalent to the use of flux equations for mass and vertical momentum, and that the latter pair is to be preferred.