Cross-correlation in a turbulent flow: Analysis of the velocity field using the ρ_DCCA coefficient

¹ Federal Institute of Bahia - Paulo Afonso, Bahia, Brazil
² Federal Institute of Bahia - Camaçari, Bahia, Brazil
³ Unijorge University Center - Salvador, Bahia, Brazil
⁴ Federal University of Bahia - Salvador, Bahia, Brazil
⁵ Computational Modeling Program, SENAI CIMATEC - Salvador, Bahia, Brazil
⁶ National Institute for Science and Technology - Petroleum Geophysics, INCT-GP - Salvador, Bahia, Brazil
⁷ Department of Physics, State University of Feira de Santana - Feira de Santana, Bahia, Brazil
⁸ Earth Sciences and Environment Modeling Program, State University of Feira de Santana Feira de Santana, Bahia, Brazil
⁹ Pursuelife - Consultancy on Applied Science - Salvador, Bahia, Brazil

Received: 24 May 2018
Accepted: 25 July 2018

Abstract

The stochastic process of a turbulent flow in a pipeline provides a time series of the velocity field at any point of the domain by solving numerically the Navier-Stokes equation. The turbulent flow was produced by obstacles near the inlet, injecting eddies into the current. Moving downstream, these eddies evolve to a fully turbulent flow. Many length and time scales are involved in this process. We explore the cross-correlations of the velocity field time series at different points and also at different time scales using the detrended cross-correlation coefficient, ρ_DCCA, designed to analyze the cross-correlations in non-stationary time series. Thus, the results with ρ_DCCA allow interpreting how these eddies propagate downstream, and also quantify how adherent the velocity fields are with respect to the pipeline position.