Research Article Dynamical Simulation and Statistical Analysis of Velocity Fluctuations of a Turbulent Flow behind a Cube

A statistical approach for the treatment of turbulence data generated by computer simu-lations is presented. A model for compressible flows at large Reynolds numbers and low Mach numbers is used for simulating a backward-facing step airflow. A scaling analy-sis has justified the commonly used assumption that the internal energy transport due to turbulent velocity fluctuations and the work done by the pressure field are the only relevant mechanisms needed to model subgrid-scale flows. From the numerical simula-tions, the temporal series of velocities are collected for ten different positions in the flow domain, and are statistically treated. The statistical approach is based on probability av-erages of the flow quantities evaluated over several realizations of the simulated flow. We look at how long of a time average is necessary to obtain well-converged statistical results. For this end, we evaluate the mean-square difference between the time average and an ensemble average as the measure of convergence. This is an interesting question since the validity of the ergodic hypothesis is implicitly assumed in every turbulent flow simula-tion and its analysis. The ergodicity deviations from the numerical simulations are com-pared with theoretical predictions given by scaling arguments. A very good agreement is observed. Results for velocity fluctuations, normalized autocorrelation functions, power spectra, probability density distributions, as well as skewness and flatness coefficients are also presented. Copyright © 2007 T. F. Oliveira et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1