  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.
