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

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, ρDCCA , designed to analyze the cross-correlations in non-stationary time series. Thus, the results with ρDCCA allow interpreting how these eddies propagate downstream, and also quantify how adherent the velocity fields are with respect to the pipeline position.