A similarity scaling model for the axisymmetric turbulent jet based on first principles

Abstract

Similarity scaling, when it can be justified, is a powerful tool for predicting properties of fluid flows and reducing the computational load when using mathematical models. Numerous publications describe different applications of this method, using often different scaling laws with one or more scaling parameters. The justification for these laws is often based on some assumptions or references to experimental results. In this paper, we base the scaling law on basic physical principles of classical Newtonian physics (Galilei group) and derive some predictions that we apply to a simple model for the axisymmetric turbulent jet. In a companion paper, we compare these predictions to careful measurements on a free jet in the laboratory and evaluate how far our model predictions are borne out by the experimental results. We have succeeded in obtaining such high-measurement quality that we can compute both second- and third-order statistical functions even far downstream and far-off axis. We can already here reveal that we find very good agreement between a simple one-parameter geometric scaling law derived from the model and numerous first-order and higher-order statistical results computed from the experimental data.