Quasi-Lagrangian studies of spatio-temporal correlation in incompressible MHD turbulence

Turbulence is of fundamental importance for many physical systems on Earth and throughout the universe. A turbulent flow can be described as the superposition of turbulent fluctuations of various length scales, which interact with each other non-linearly, leading to a transfer of energy across scales. We aim at a better understanding of the temporal and spatial properties of this energy transfer process in plasma turbulence, by studying the spatio-temporal correlation between turbulent structures in magnetohydrodynamic (MHD) turbulence.

To this end we perform three-dimensional direct numerical simulations with a pseudo-spectral method. We employ the quasi-Lagrangian reference frame, in which tracer particles are followed in the flow each carrying with it a set of probes at fixed distances across which the fluctuations are computed. This avoids the large-scale sweeping effect, which in the case of fixed-grid (Eulerian) measurements would obscure the small-scale temporal dynamics. This approach is based on previous studies in Navier-Stokes turbulence [Physics of Fluids 23.8 (2011): 085107] and has been extended to account for the magnetic field.

We investigate systems with different mean magnetic field strength. The spatio-temporal correlation functions yield insight into the nature of the cross-scale transfer of energy in terms of the direction, strength, and time scale of the transfer process. In particular, the scaling of the correlation times perpendicular and parallel to the local magnetic field, the influence of the mean magnetic field and the implications for the current understanding of the cross-scale transfer process are discussed.