Recent developments in the statistical modelling of turbulent flows

Statistical methods are often used to describe transport processes in turbu lent reacting flows. However, in many cases of practical relevance one has to consider not only such transports but also their influence on the turbul ent reacting flow. Just the simulation of such interactions could not be pr ovided by approaches applied previously. this led, e.g., in respect to the atmospheric chemistry, to considerable problems because nonlinear chemical conversion processes, which appear nearly in all cases of practical interes t, between emissions and species that are distributed in the ambient flow c ould only be treated approximately. To overcome these problems, methods are needed that are able to describe not only transport processes but addition ally the turbulence. The developments of such techniques requires solutions for three problems: First, suited equations have to be derived that are ir t consistency with the hydrodynamic equations, second the capability of suc h methods has to be demonstrated to reflect the features of complex turbule nt flows, and third, it has to be shown that the computational costs of suc h methods are acceptable. It is described here, in which way these problems could be solved recently, and which advantages arise from the application of such advanced statistical methods.