An open source package to perform basic and advanced statistical analysis of turbulence data and other complex systems

Abstract

We present an open-source package that helps the user to perform a basic statistical analysis of a given turbulence dataset. We believe that this package is useful to the entire turbulence community. It can be used to estimate statistical quantities of turbulence such as the spectral density, turbulence intensity, integral length scale, Taylor microscale, Kolmogorov scale, and dissipation rate as well as velocity increments, structure functions, and their scaling exponents. Different well-known methods available in the literature were selected so that they can be compared. This package also performs an advanced analysis that includes the scale-dependent statistical description of turbulent cascade using the Fokker–Planck equation, consequently leading to the assessment of integral fluctuation theorems. As a precondition for the stochastic process approach, Markovian properties of the turbulent cascade in scale are tested. This is utilized to estimate the drift and diffusion coefficients of the Fokker–Planck equation. The total entropy production for each independent cascade trajectory can be determined using a Fokker–Planck equation. Estimating total entropy production admits a rigorous law of non-equilibrium stochastic thermodynamics, namely, the integral fluctuation theorem, which must be valid if Markov properties hold and the Fokker–Planck equation is correct. This approach to the turbulent cascade process has the potential for a new way to link the statistical description of turbulence, non-equilibrium stochastic thermodynamics, and local turbulent flow structures. Finally, we emphasize that the presented package can be used for the analysis of other data with turbulent-like complexity as well.