TURB-MHD: an open-access database of forced homogeneous magnetohydrodynamic turbulence

TL;DR

The paper introduces TURB-MHD, an open-access database of six forced, homogeneous, three-dimensional incompressible MHD turbulence simulations, enabling broad spectral analyses and a posteriori LES validation. It combines standard and hyperdiffusive dissipation in a triply periodic domain with band-limited forcing and varied background magnetic fields to realize forward energy cascades and, under strong background fields, partial inverse kinetic cascades. The authors describe the DNS methodology, dataset provenance, and data-access workflow, including Fourier-space field dumps and tools to reconstruct real-space fields, provided via the SMART-Turb portal. The work delivers a reproducible resource for examining energy transfer across scales, magnetic-field influence on structure, and sub-grid modeling in MHD turbulence, with potential for extensive validation and cross-study comparisons.

Abstract

We present TURB-MHD, a database formed by six datasets of three-dimensional incompressible homogeneous magnetohydrodynamic turbulence maintained by a large-scale random forcing with minimal injection of cross helicity. Five of them describe a stationary state including one characterised by a weak background magnetic field. The remaining dataset is non-stationary and is featured by a strong background magnetic field. The aim is to provide datasets that clearly exhibit the phenomenon of the total energy cascade from the large to the small scales generated by the large-scale energy injection and one showing a partial inverse kinetic energy cascade from the small to the large scales. This database offers the possibility to realize a wide variety of analyses of fully developed magnetohydrodynamic turbulence from the sub-grid scale filtering up to the validation of an a posteriori LES. TURB-MHD is available for download using the SMART-Turb portal http://smart-turb.roma2.infn.it.

Figures (7)

• Figure 1: 3D visualization where each horizontal panel is formed by three visualization cubes showing $u_x$ and the magnitude of $\bm{j} = \nabla \times \bm{b}$ as a function of the position $(\bm{x},\bm{y}$, $\bm{z})$. Top panel $B_0=0$, middle panel $B_0=1.2 \, B_{rms}$ and bottom panel $B_0=12.7 \, B_{rms}$. In each visualisation the colour range is shared between the configuration. Although the colour ranges are the same, the bottom left panels shows a more intense colouring due to the higher kinetic energy, see table \ref{['tab:datasets']}.
• Figure 2: Time-averaged omnidirectional spectra for the velocity and magnetic field, respectively $E_u(k)$ and $E_b(k)$ normalised by the the product between the mean total energy and the forcing scale, both indicated in table \ref{['tab:datasets']}, as functions of the adimensional variable $k / k_f = L_f/\ell$: (a) comparison between datasets A1 and A3, (b) between datasets A2 and A4 while (c) and (d) refers to dataset C1 and C10 respectively. The gray region indicates the wavenumber band $k \in [2.5,5.0]$ where the velocity field is forced.
• Figure 3: Time evolution of global observables for datasets A1 and A3. Left panel: Time evolution of mean kinetic and magnetic energy normalised by the mean total energy. Right panel: mean kinetic and Joule dissipation rate normalised by the total energy dissipation. The red dots correspond to the sampled velocity and magnetic field configurations.
• Figure 4: Time evolution of global observables for datasets A2 and A4. The y-axes ranges are the same as those in fig. \ref{['fig:hyperv_1024']}.
• Figure 5: Analogously to fig. \ref{['fig:hyperv_1024']}, time evolution of global observables for dataset C1. To improve the clarity of the picture, the red markers indicating the sampled configurations in the magnetic field have been omitted to provide better clarity of the timeseries. In addition, for clarity sake, the y-axis range of the left panel is narrower than that of the corresponding left panels above.