The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck

TL;DR

This paper shows that the Lagrangian-averaged MHD alpha-model accurately captures turbulence properties without bottleneck effects, enabling significant computational savings compared to direct simulations.

Contribution

It demonstrates that LAMHD reproduces turbulence features effectively without bottleneck issues, unlike the neutral fluid case, allowing large reductions in computational resources.

Findings

No super-filter bottleneck effect in LAMHD

200-fold reduction in computational degrees of freedom

Accurate reproduction of large and small-scale turbulence properties

Abstract

We demonstrate that, for the case of quasi-equipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics alpha-model (LAMHD) reproduces well both the large-scale and small-scale properties of turbulent flows; in particular, it displays no increased (super-filter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the sub-filter-scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha-model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of super-filter-scale spectral properties. No such regions are found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of 200 when compared to a direct numerical simulation on a large grid of 1536^3 points at the same Reynolds number.