Towards better uncertainty estimates for turbulence statistics

Abstract

 Methods for calculating the statistical uncertainty associated with the sampling of random processes such as those which occur in turbulence research are given. In particular, formulas based on normal distribution assumptions and on any general distribution shape are given for means, variances, Reynolds stresses, correlation coefficients, homogeneous and mixed turbulent triple products and fourth order turbulence moments. In addition, two resampling algorithms, the “bootstrap” and “jackknife”, are presented and compared using actual turbulence data. The availability of these methods will allow turbulence data to be presented with statistical uncertainty error bars on all turbulence quantities.