Towards a turbulent modeling of rapid flow of granular materials

From the global equations of balance for particulate media and via a special ensemble averaging technique, the local equations governing the mean motion and the random fluctuations in a rapid flow of granular materials are derived. The resulting equations resemble those of a compressible turbulent flow. Approximate expressions for the components of the fluctuation stress tensor are obtained which are completely computable and in this sense are rather new. The order of magnitude analysis of these stresses indicate that they are in complete agreement with available experimental results. Furthermore, an explicit equation is derived for the evolution and transport of random fluctuation energy which is coupled with the energy dissipation due to fluctuating stress tensor and the mean motion.