Structures in magnetohydrodynamic turbulence: detection and scaling

We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stems from numerical simulations of decaying three-dimensional (3D) magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536^3 points, and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X-point configuration embedded in 3D, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8,000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with MHD. We suggest that this range can be governed by turbulence dynamics as opposed to criticality, and propose an interpretation of intermittency in terms of propagation of local instabilities.Comment: 17 pages, 9 figures, 5 table

Sub-grid effects of the Voigt viscoelastic regularization of a singular dyadic model of turbulence

In this work we investigate the spectral signature of Navier–Stokes–Voigt (NSV) viscoelastic fluid flows by employing numerical simulations of a singular dyadic shell model. Our results clearly show that as the relaxation time is increased above a threshold, the inertial range is reduced, conserving part of the large-scale statistics. These results differ drastically from the two power-law scenarios observed in a previous work, where the NSV model was studied via Sabra shell model simulations instead. We also show that the additional elastic term regularizes the singular dyadic model, which is the main reason behind this reduction of degrees of freedom. The results of this work aim at proposing the NSV regularization as a sub-grid model.Indisponível

Spectrally-Consistent Regularization of Navier–Stokes Equations

This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at:https://doi.org/10.1007/s10915-018-0880-x ".The incompressible Navier–Stokes equations form an excellent mathematical model for turbulent flows. However, direct simulations at high Reynolds numbers are not feasible because the convective term produces far too many relevant scales of motion. Therefore, in the foreseeable future, numerical simulations of turbulent flows will have to resort to models of the small scales. Large-eddy simulation (LES) and regularization models are examples thereof. In the present work, we propose to combine both approaches in a spectrally-consistent way: i.e. preserving the (skew-)symmetries of the differential operators. Restoring the Galilean invariance of the regularization method results into an additional hyperviscosity term. In this way, the convective production of small scales is effectively restrained whereas the destruction of the small scales is enhanced by this hyperviscosity effect. This approach leads to a blending between regularization of the convective term and LES. The performance of these improvements is assessed through application to Burgers’ equation, homogeneous isotropic turbulence and a turbulent channel flow.Peer ReviewedPostprint (author's final draft