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

Abstract

We present a user-friendly open-source MATLAB\textsuperscript{\textregistered} package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg. Firstly, this package helps the user to perform a very basic statistical analysis of a given turbulent data set which we believe to be useful to the entire turbulence community. It can be used to estimate the statistical quantities of turbulence such as the spectrum density, turbulent intensity, integral length scale, Taylor microscale, Kolmogorov scale and dissipation rate. Different well-known methods available in the literature were selected so that they can be compared. Secondly, this package also performs an advanced analysis which includes the scale-dependent statistical description of turbulent cascade using the Fokker-Planck equation which consequently leads to the assessment of integral fluctuation theorem. This is utilized to estimate velocity increments, structure functions and their scaling exponents, drift and diffusion coefficients of the Fokker-Planck equation and consequently the total entropy production of the turbulent cascade. As a precondition for the stochastic process approach, Markovian properties of the turbulent cascade in scale are tested. The knowledge of a Fokker-Planck equation allows to determine for each independent cascade trajectories a total entropy production. The estimation of total entropy production allows to verify 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.