A priori analysis of coarse-grained approaches in wall turbulence

The aim of this thesis work is the analysis of different approaches to the simulation in the context of wall turbulence. The final goal is the a priori characterization of the quantities related to a Large Eddy Simulation (LES) with different filter types and filtering lengths, starting from a Direct Numerical Simulation (DNS). The paradigmatic flow chosen for this analysis is the channel flow at a Friction Reynolds Number $Re_\tau = 1000$. The intrinsic symmetries of this configuration guarantee simplicity in the calculation of the quantities related to the flow. The choice of this Reynolds number has been taken as it constitutes a good trade-off for the description of physical phenomena and the computational cost. The idea behind this work is the determination of the sub-grid stress tensor and sub-grid dissipation related to two different filter lengths and the consequent identification of eventual back-scatter phenomena. Those phenomena picture the energy transfer from sub-grid scales to resolved scales, in the areas where this happens, the sub-grid dissipation has a positive contribution to the turbulent kinetic energy equation, namely it contributes as production. This behavior is apparently unphysical; however, it is an indication of a very coarse filtering in that area, from which comes an indication of the possible need of re-adapting the filter length. The successive analysis of those quantities with respect to the DNS from which the data are taken gives a guideline for the study a priori of the LES approach. A complete characterization of the DNS flow with the evaluation of the classical flow statistics, exploiting the Reynolds decomposition, and of the turbulent kinetic energy budget equation in all its components created a benchmark for the comparison of the filtered data. Two different filter kernels have been analyzed: Top-Hat filter and Gaussian filter. Their characteristic spectra differ, and those differences have been addressed in this thesis work. The filter length is also a key parameter, and the choice has been taken as a function of wall units, with a differentiation on the streamwise and spanwise directions. The two couples of chosen filter lengths are the following: $\Delta x^+ = 80$ and $\Delta y^+ = 40$, and $\Delta x^+ = 40$ and $\Delta y^+ = 20$. The results pictured back-scatter for all the configurations and the characterization of the filtered TKE equation terms allowed a comprehension a priori of the possible LES approach.