Modelling and analysis of turbulent datasets using Auto Regressive Moving Average processes
- Laboratoire SPHYNX, Service de Physique de l'Etat Condensé, DSM, CEA Saclay, CNRS URA 2464, 91191 Gif-sur-Yvette (France)
- Dipartimento di Scienze Statistiche, Universitá di Bologna, Via delle Belle Arti 41, 40126 Bologna (Italy)
- Institut de Recherche sur les Phénomènes Hors Equilibre, Technopole de Chateau Gombert, 49 rue Frédéric Joliot Curie, B.P. 146, 13 384 Marseille (France)
- Université Paris Diderot - LIED - UMR 8236, Laboratoire Interdisciplinaire des Énergies de Demain, Paris (France)
- Laboratoire FAST, CNRS, Université Paris-Sud (France)
We introduce a novel way to extract information from turbulent datasets by applying an Auto Regressive Moving Average (ARMA) statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded time series to a discrete version of a stochastic differential equation which is able to describe the correlation structure in the dataset. We introduce a new index Υ that measures the difference between the resulting analysis and the Obukhov model of turbulence, the simplest stochastic model reproducing both Richardson law and the Kolmogorov spectrum. We test the method on datasets measured in a von Kármán swirling flow experiment. We found that the ARMA analysis is well correlated with spatial structures of the flow, and can discriminate between two different flows with comparable mean velocities, obtained by changing the forcing. Moreover, we show that the Υ is highest in regions where shear layer vortices are present, thereby establishing a link between deviations from the Kolmogorov model and coherent structures. These deviations are consistent with the ones observed by computing the Hurst exponents for the same time series. We show that some salient features of the analysis are preserved when considering global instead of local observables. Finally, we analyze flow configurations with multistability features where the ARMA technique is efficient in discriminating different stability branches of the system.
- OSTI ID:
- 22310806
- Journal Information:
- Physics of Fluids (1994), Vol. 26, Issue 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-6631
- Country of Publication:
- United States
- Language:
- English
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