arXiv subjects

Neco Kriel

Publications and source records attributed to Neco Kriel.

9 recordsLinked to original sources

arXiv2026

Magnetising the quokka code with fast, second-order accurate, error-correcting schemes for magnetohydrodynamics on GPUs

We implement a second-order accurate constrained transport (CT) magnetohydrodynamics (MHD) module with first-order flux correction in the open-source, adaptive mesh refinement (AMR), GPU-accelerated code quokka, supporting both ideal and resistive (constant Ohmic) regimes. For computing and averaging the electromotive forces (EMFs) at cell edges, the basis of any CT-MHD method, we experiment with a wide range of recent, state-of-the-art schemes, together with different reconstruction schemes. Alongside these, we develop a new EMF compute scheme that requires fewer reconstruction steps than existing approaches. We evaluate these scheme combinations on the basis of accuracy, stability, and GPU throughput, and demonstrate that our new scheme achieves accuracy comparable to the best-in-class existing methods, together with greater stability in reconnection-dominated flows and roughly 25--60% higher GPU throughput. Using this scheme, quokka achieves excellent results across a wide range of MHD flow regimes, reaching >50 million cell updates per GPU per second, with >70% parallel efficiency out to >500 GPUs. Finally, we confirm that our CT implementation preserves divergence-free magnetic fields (to machine precision) under AMR.

astro-ph.IM↗

arXiv2025

Conservation of magnetic-helicity fluctuations due to spatial decorrelation of fluxes in decaying MHD turbulence

Hosking & Schekochihin (2021, Phys. Rev. X 11, 041005) have proposed that statistically isotropic decaying MHD turbulence without net magnetic helicity conserves the mean square fluctuation level of magnetic helicity in large volumes -- or, equivalently, the integral over space of the two-point correlation function of the magnetic-helicity density, denoted $I_H$. Formally, the conservation and gauge invariance of $I_H$ require the vanishing of certain boundary terms related to the strength of long-range spatial correlations. These boundary terms represent the ability (or otherwise) of the turbulence to organise fluxes over arbitrarily large distances to deplete or enhance fluctuations of magnetic helicity. In this work, we present a theory of these boundary terms, employing a methodology analogous to that of Batchelor & Proudman (1956, Philos. Trans. R. Soc. A 248, 369) to determine the relevant asymptotic forms of correlation functions. We find that long-range correlations of sufficient strength to violate the conservation of $I_H$ cannot develop dynamically if the evolution equation for the magnetic vector potential is chosen to be local in space. Likewise, we find that such correlations cannot develop for a wide class of gauge choices that make this equation non-local (including the Coulomb gauge). Nonetheless, we also identify a class of non-local gauge choices for which correlations that are sufficiently strong to violate the conservation of $I_H$ do appear possible. We verify our theoretical predictions for the case of the Coulomb gauge with measurements of correlation functions in a high-resolution numerical simulation.

physics.flu-dyn↗

arXiv2025

The universal growth of magnetic energy during the nonlinear phase of subsonic and supersonic small-scale dynamos

Small-scale dynamos (SSDs) amplify magnetic fields in turbulent plasmas. Theory predicts nonlinear magnetic energy growth $E_\mathrm{mag} \propto t^{p_\mathrm{nl}}$, but this scaling has not been tested across flow regimes. Using a large ensemble of SSD simulations spanning subsonic to supersonic turbulence, we measure linear growth ($p_\mathrm{nl} = 1$) in subsonic flows and quadratic growth ($p_\mathrm{nl} = 2$) in supersonic flows. In all cases, the nonlinear dynamo converts a nearly constant fraction $\sim 1/100$ of the turbulent kinetic energy flux into magnetic energy, and the nonlinear phase has a characteristic duration $\Delta t \approx 20\,t_0$, where $t_0$ is the outer-scale turnover time. By isolating the onset of magnetic backreaction in SSDs, our statistical ensemble approach identifies a robust efficiency and duration for the nonlinear SSD that can be used to interpret more complex astrophysical and laboratory plasmas.

physics.plasm-ph↗

arXiv2023

Taking control of compressible modes: bulk viscosity and the turbulent dynamo

Many polyatomic astrophysical plasmas are compressible and out of chemical and thermal equilibrium, introducing a bulk viscosity into the plasma via the internal degrees of freedom of the molecular composition, directly impacting the decay of compressible modes, $\mathbf{v}_{\parallel}(\mathbf{k})$. This is especially important for small-scale, turbulent dynamo processes in the interstellar medium, which are known to be sensitive to the effects of compression. To control the viscous properties of $\mathbf{v}_{\parallel}(\mathbf{k})$, we perform trans-sonic, visco-resistive dynamo simulations with additional bulk viscosity $\nu_{\rm bulk}$, deriving a new $\nu_{\rm bulk}$ Reynolds number $\rm{Re}_{\rm bulk}$, and viscous Prandtl number $\rm{P}\nu \equiv \rm{Re}_{\rm bulk} / \rm{Re}_{\rm shear}$, where $\rm{Re}_{\rm shear}$ is the shear viscosity Reynolds number. We derive a framework for decomposing $E_{\rm mag}$ growth rates into incompressible and compressible terms via orthogonal tensor decompositions of $\nabla\otimes\mathbf{v}$, where $\mathbf{v}$ is the fluid velocity. We find that $\mathbf{v}_{\parallel}(\mathbf{k})$ play a dual role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the main driver of growth, even in compressible dynamos. In the absence of $\nu_{\rm bulk}$ ($\rm{P}\nu \to \infty$), $\mathbf{v}_{\parallel}(\mathbf{k})$ pile up on small-scales, creating a spectral bottleneck, which disappears for $\rm{P}\nu \approx 1$. (abridged). We emphasize the importance of further understanding the role of $\nu_{\rm bulk}$ in compressible astrophysical plasmas, which we estimate could be as strong as the shear viscosity in the cold ISM, and highlight that compressible direct numerical simulations without bulk viscosity have unresolved compressible mode dissipation scales.

astro-ph.GA↗

arXiv2023

Fundamental MHD scales -- II: the kinematic phase of the supersonic small-scale dynamo

Many astrophysical small-scale dynamos (SSDs) amplify weak magnetic fields via highly compressible, supersonic turbulence, but established SSD theories have overlooked these compressible effects. To address this, we perform visco-resistive SSD simulations across a range of sonic Mach numbers ($\mathcal{M}$), hydrodynamic Reynolds numbers ($\mathrm{Re}$), and magnetic Prandtl numbers ($\mathrm{Pm}$). We develop robust methods to measure kinetic and magnetic energy dissipation scales ($\ell_\nu$ and $\ell_\eta$) and the scale of strongest magnetic fields ($\ell_\mathrm{p}$) during the kinematic phase. We demonstrate that $\ell_\nu/\ell_\eta \sim \mathrm{Pm}^{1/2}$ is a universal feature for $\mathrm{Pm} \geq 1$ SSDs, regardless of $\mathcal{M}$ or $\mathrm{Re}$. Incompressible SSDs (either $\mathcal{M} \leq 1$ or $\mathrm{Re} < \mathrm{Re}\mathrm{crit} \approx 100$) concentrate magnetic energy at $\ell_\mathrm{p} \sim \ell_\eta$ with inversely correlated field strength and curvature. However, for compressible SSDs ($\mathcal{M} > 1$ and $\mathrm{Re} > \mathrm{Re}\mathrm{crit}$), shocks concentrate magnetic energy in large structures with $\ell_\mathrm{p} \sim (\ell_\mathrm{turb} / \ell_\mathrm{shock})^{1/3} \ell_\eta \gg \ell_\eta$, where $\ell_\mathrm{shock}$ is the characteristic shock width, and $\ell_\mathrm{turb}$ is the outer scale of the turbulent field. In this regime, magnetic field-line curvature becomes nearly independent of field strength. These results have implications for galaxy mergers and cosmic ray transport models in the interstellar medium.

astro-ph.GA↗

arXiv2023

Growth or Decay -- I: universality of the turbulent dynamo saturation

The turbulent small-scale dynamo (SSD) is likely to be responsible for the magnetisation of the interstellar medium (ISM) that we observe in the Universe today. The SSD efficiently converts kinetic energy $E_{\rm kin}$ into magnetic energy $E_{\rm mag} $, and is often used to explain how an initially weak magnetic field with $E_{\rm mag} \ll E_{\rm kin}$ is amplified, and then maintained at a level $E_{\rm mag} \lesssim E_{\rm kin}$. Usually, this process is studied by initialising a weak seed magnetic field and letting the turbulence grow it to saturation. However, in this Part I of the Growth or Decay series, using three-dimensional, visco-resistive magnetohydrodynamical turbulence simulations up to magnetic Reynolds numbers of 2000, we show that the same final state in the integral quantities, energy spectra, and characteristic scales of the magnetic field can also be achieved if initially $E_{\rm mag} \sim E_{\rm kin}$ or even if initially $E_{\rm mag} \gg E_{\rm kin}$. This suggests that the final saturated state of the turbulent dynamo is set by the turbulence and the material properties of the plasma, independent of the initial structure or amplitude of the magnetic field. We discuss the implications this has for the maintenance of magnetic fields in turbulent plasmas and future studies exploring the dynamo saturation.

astro-ph.GA↗

arXiv2022

Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field

Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $δ\mathbf{B}$ and large-scale, $\mathbf{B}_0$ fields, $\left< (δ\mathbf{B}\cdot\mathbf{B}_0)^{2} \right>^{1/2}_{\mathcal{V}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible MHD turbulence. Furthermore, we explore the relation between the turbulent, mean-field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetised ISM.

astro-ph.GA↗

arXiv2022

Fundamental scales in the kinematic phase of the turbulent dynamo

The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, $k_{\rm p}$, do magnetic fields become most concentrated? There has been some disagreement about whether $k_{\rm p}$ is controlled by the viscous scale, $k_ν$ (where turbulent kinetic energy dissipates), or the resistive scale, $k_η$ (where magnetic fields dissipate). Here we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run $104$-simulations with hydrodynamic Reynolds numbers of $10 \leq {\rm Re} \leq 3600$, and magnetic Reynolds numbers of $270 \leq {\rm Rm} \leq 4000$, to explore the dependence of $k_{\rm p}$ on $k_ν$ and $k_η$. Using physically motivated models for the kinetic and magnetic energy spectra, we measure $k_ν$, $k_η$ and $k_{\rm p}$, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_ν= (0.025^{+0.005}_{-0.006})\, k_{\rm turb}\, {\rm Re}^{3/4}$ and $k_η= (0.88^{+0.21}_{-0.23})\, k_ν\, {\rm Pm}^{1/2}$, where $k_{\rm turb}$ is the turbulence driving wavenumber and ${\rm Pm}={\rm Rm}/{\rm Re}$ is the magnetic Prandtl number. We demonstrate that the principle dependence of $k_{\rm p}$ is on $k_η$. For plasmas where ${\rm Re} \gtrsim 100$, we find that $k_{\rm p} = (1.2_{-0.2}^{+0.2})\, k_η$, with the proportionality constant related to the power-law `Kazantsev' exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where ${\rm Re} > 100$, compared to ${\rm Re} < 100$. We report a minimum critical hydrodynamic Reynolds number, ${\rm Re}_{\rm crit} = 100$ for bonafide turbulent dynamo action.

astro-ph.SR↗

arXiv2019

Is The Starry Night Turbulent?

Vincent van Gogh's painting, The Starry Night, is an iconic piece of art and cultural history. The painting portrays a night sky full of stars, with eddies (spirals) both large and small. \cite{Kolmogorov1941}'s description of subsonic, incompressible turbulence gives a model for turbulence that involves eddies interacting on many length scales, and so the question has been asked: is The Starry Night turbulent? To answer this question, we calculate the azimuthally averaged power spectrum of a square region ($1165 \times 1165$ pixels) of night sky in The Starry Night. We find a power spectrum, $\mathcal{P}(k)$, where $k$ is the wavevector, that shares the same features as supersonic turbulence. It has a power-law $\mathcal{P}(k) \propto k^{-2.1\pm0.3}$ in the scaling range, $34 \leq k \leq 80$. We identify a driving scale, $k_\text{D} = 3$, dissipation scale, $k_ν= 220$ and a bottleneck. This leads us to believe that van Gogh's depiction of the starry night closely resembles the turbulence found in real molecular clouds, the birthplace of stars in the Universe.

physics.pop-ph↗