Recurrence quantification analysis of MHD turbulent channel flow

Abstract

We present Recurrence Plots (RPs) and Recurrence Quantification Analysis (RQA) of time series of velocities in a low-Reynolds-number magnetohydrodynamic turbulent channel flow. The flow was simulated using a fully spectral code with Fourier and Chebyshev decomposition in the periodic and wall bounded directions, respectively. Direct numerical simulations of the flow were performed for Reτ=180, based on the friction velocity and the channel half-height, for the hydrodynamic flow and in the case of a streamwise magnetic field with magnetic interaction number 0.1. The turbulent velocity time series of both cases of the flow were recorded at several positions in the wall-normal direction at fixed spanwise and streamwise positions and analyzed along all directions using RPs and RQA. Using this approach, a number of different flow regions were identified depending on the distance from the channel walls in accordance to the turbulent boundary-layer theory. Different characteristic times were extracted for the various velocity components and related to the dynamics of the flow. Moreover, with the use of Recurrence Plots several distinct system regimes were identified and the effect of the magnetic field was localized.