A conditional sampling method based on fuzzy clustering for the analysis of large-scale dynamics in turbulent flows

Abstract

A conditional sampling technique, based on fuzzy clustering, is used to educe the organization of the secondary flow motions observed in the large-eddy simulation of a turbulent square channel flow. The data analysed are the multi-valued time series obtained from sampling the secondary velocity components at a fixed cross-section of the channel, over consecutive time steps. The mean values of the secondary flow motion velocities are one order of magnitude lower than their r.m.s values. The purpose of the conditional sampling scheme used is to replace the picture of the secondary flow motions provided by the unconditional time mean with several ensemble averages. In this way the whole variability of the instantaneous data can be split in two parts: one for the difference between the observed ensemble averages, and the other for the variability within each ensemble. Unlike other conditional sampling schemes which sort only part of the data into one or more families depending on an externally fixed condition, the fuzzy clustering approach used here first determines the optimum number of families or clusters and then classifies all the recorded time steps. The results show that the local turbulence intensities of the ensemble averages obtained from fuzzy clustering can be reduced by one order of magnitude. In addition, the classification of all the time steps into several clusters or families enables the large scale dynamics of the educed structures to be analysed.