Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence

Abstract

The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlated with regions of high strain rate $\mathbf{S}$ also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density $\mathbf{j}$. Viscous dissipation ($\propto {\mathbf{S}}^2$) as well as Ohmic dissipation ($\propto {\mathbf{j}}^2$) reside in regions where strain and rotation are locally almost in balance. The structures related to the velocity gradient possess different characteristics than those associated with the magnetic field gradient with the latter being locally more quasi-two dimensional.

21 pages, 16 figures

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• Interaction of vortex stretching with wind power fluctuations
• Statistics of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence
• Statistical Properties of three-dimensional Hall Magnetohydrodynamics Turbulence
• Extraction of invariant manifolds and application to turbulence with a passive scalar
• Magnetized Decaying Turbulence in the Weakly Compressible Taylor-Green Vortex