The given thesis is based on the turbulence theory based on Lie group methods, which has been developed in the last couple of years. With this theory at hand it is possible to derive classical semi-empirical approaches, as for example the law of the wall, from "first principles". Here three different flow cases, which are the turbulent diffusion, the zero-pressure gradient turbulent boundary layer flow and the fully developed turbulent rotating pipe flow have been investigated. Using symmetry methods linear and non-linear eddy viscosity models as well as Reynolds stress models have been analyzed. Thereby it has been checked if the model equations have the same symmetry properties as the two-point correlation equations and if they are able to describe the turbulent scaling laws which have been derived for the given flow cases. Based on these investigations conditions for the model constants and the structure of the model equations have been derived
