We suggest a new approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average modeling of turbulent time series. We introduce a new index $Upsilon$ that measures the distance from
a Kolmogorov-Obukhov model in the Auto-Regressive Moving-Average models space. Applying our analysis to Particle Image Velocimetry and Laser Doppler Velocimetry measurements in a von Karman swirling flow, we show that $Upsilon$ is proportional to the traditional intermittency correction computed from the structure function. Therefore it provides the same information, using much shorter time series. We conclude that $Upsilon$ is a suitable index to reconstruct the spatial intermittency of the dissipation in both numerical and experimental turbulent fields.
We address the problem of defining early warning indicators of critical transition. To this purpose, we fit the relevant time series through a class of linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We define two indicator
s representing the total order and the total persistence of the process, linked, respectively, to the shape and to the characteristic decay time of the autocorrelation function of the process. We successfully test the method to detect transitions in a Langevin model and a 2D Ising model with nearest-neighbour interaction. We then apply the method to complex systems, namely for dynamo thresholds and financial crisis detection.
