Decomposition of Turbulent Fluxes from Filtered Data and Application to Turbulent Premixed Combustion Modelling

The exact reconstruction of statistical quantities from filtered data is a fundamental question in turbulence research. Filtered data can be either data from a Large Eddy Simulation (LES) or it can be experimental data with insufficient resolution to capture the finest scales. Usually it is assumed that averages of filtered and unfiltered quantities are the same and as a consequence the Reynolds stress or turbulent scalar flux is traditionally split in a resolved part and a mean subfilter part. However, this decomposition holds only true for homogeneous flows without mean gradients as demonstrated recently (Klein and Germano [1]). In this work an exact relation between filtered, respectively Favre filtered, and unfiltered turbulent fluxes will be derived and tested in the context of turbulent premixed combustion, where heat release gives locally rise to strong gradients and consequently the failure of the standard assumption is expected. For demonstration of the problem, filtered data will be considered from a purely mathematical point of view by applying a convolution operation to data representing solutions to the Navier-Stokes Equations. Results will be discussed for the subfilter stress, the turbulent scalar flux and the subfilter scalar variance.