Mixed Averaging Procedures
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Fundamental in the numerical simulation of coarse graining turbulence are the filtering operator that represents explicitly or implicitly the coarseness of the representation, and the statistical operator that is used to reduce information and to extract significant quantities from the chaotic database produced by the computation. The statistical operator usually applied in postprocessing a numerical database is a mixture of physical averages in time, for steady turbulence, and in homogeneous space directions. Other averaging operators could be phase or ensemble averages over different simulations of the same flow. In this paper we propose simple measures of the relative importance of such averages based on a multiscale analysis of the variance, and we apply our new indicators to three steady turbulent flows homogeneous in the spanwise direction. The work can be used to identify the most effective averaging procedure in flow configurations characterized by at least two homogeneous directions. Thus it will contribute to either achieving better statistics for turbulent flow predictions or to reduce computing time.
