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

A statistical approach for the treatment of turbulence data generatedby computer simulations is presented. A model for compressible flowsat large Reynolds numbers and low Mach numbers is used forsimulating a backward-facing step airflow. A scaling analysis hasjustified the commonly used assumption that the internal energytransport due to turbulent velocity fluctuations and the work doneby the pressure field are the only relevant mechanisms needed tomodel subgrid-scale flows. From the numerical simulations, thetemporal series of velocities are collected for ten differentpositions in the flow domain, and are statistically treated. Thestatistical approach is based on probability averages of the flowquantities evaluated over several realizations of the simulatedflow. We look at how long of a time average is necessary to obtainwell-converged statistical results. For this end, we evaluate themean-square difference between the time average and an ensembleaverage as the measure of convergence. This is an interestingquestion since the validity of the ergodic hypothesis is implicitlyassumed in every turbulent flow simulation and its analysis. Theergodicity deviations from the numerical simulations are comparedwith theoretical predictions given by scaling arguments. A very goodagreement is observed. Results for velocity fluctuations, normalizedautocorrelation functions, power spectra, probability densitydistributions, as well as skewness and flatness coefficients arealso presented