Connections between Lagrangian stochastic models and the closure theory of turbulence for stratified flows

An overview is given over some recently obtained results in the development of Lagrangian probability density function (pdf) methods for stratified turbulent flows. Turbulence is described by this approach as stochastic motion of particles and change of their properties in accord with usual budget equations of turbulence up to second-order. This approach is able to take reactions exactly into account, which is one of the essential differences to Reynolds-averaged equations. The extension of this pdf approach to stratified turbulent flows is considered here in particular with respect to scaling questions. This is illustrated by considering the buoyant plume rise as an example for turbulent mixing processes and the derivation of third-order moments of the velocity and temperature fields. Finally, the advantages of applying such concepts to modelling transport, mixing and reaction of substances in stratified flows are pointed out.