Środowiskowe Seminarium Fizyki Atmosfery

Although the evolution of turbulent velocity field is governed by the deterministic Navier-Stokes equations, due to its sensitivity to small variations in the initial and boundary conditions turbulent field may be treated as a stochastic field. For its statistical description joint probability density functions (pdf's) of velocities in different points of the flow are needed. Transport equations for such pdf's form a system of infinitely many equations where in the n-th equation for n-point pdf an unknown pdf in (n+1) points is present.In this respect, statistical turbulence closures like, e.g. k-ε or the Reynolds-stress models (RSM) provide only very limited information on a turbulent stochastic field. The Reynolds-stresses are one-point second-order moments of turbulent velocity, hence, the effect of all higher-order and multipoint correlations have to be replaced by a proper closure. Analogously, in Large Eddy Simulations (LES) a closure for the correlations on subgrid scales is sought for.In the first part of the talk theoretical description of turbulent flows and mathematical analysis of the infinite system for pdf's with the use of the Lie-group method will be addressed. Next, possible applications of this theoretical study for the modelling of turbulence will be discussed.