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We investigated incompressible and compressible magnetohydrodynamic (MHD) energy cascade rates in the solar wind at different heliocentric distances. We used in situ magnetic field and plasma observations provided by the Parker Solar Probe (PSP) mission and exact relations in fully developed turbulence. To estimate the compressible cascade rate, we applied two recent exact relations for compressible isothermal and polytropic MHD turbulence, respectively. Our observational results show a clear increase of the absolute value of the compressible and incompressible cascade rates as we get closer to the Sun. Moreover, we obtained an increase in both isothermal and polytropic cascade rates with respect to the incompressible case as compressibility increases in the plasma. Further discussion about the relation between the compressibility and the heliocentric distance is carried out. Furthermore, we compared both exact relations as compressibility increases in the solar wind and although we note a slightly trend to observe larger cascades using a polytropic closure, we obtained essentially the same cascade rate in the range of compressibility observed. Finally, we investigated the signed incompressible and compressible energy cascade rates and its connection with the real cascade rate., Comment: 23 pages. arXiv admin note: text overlap with arXiv:2102.11781

We present a high-order numerical study of the dependence of the dynamo onset on different electromagnetic boundary conditions, in convecting Boussinesq flows forced by a temperature gradient. Perfectly conducting boundaries, vacuum, and mixed electromagnetic boundary conditions are considered, using a method that treats fields and boundary conditions with close to spectral accuracy. Having one or two conducting boundaries greatly facilitates dynamo action. For the mixed case it is shown that the critical magnetic Reynolds number becomes independent of the Rayleigh number, Ra, for sufficiently large Ra.

The effect of precession in a rotating sphere filled with fluid was studied with direct numerical simulations, both in the incompressible hydrodynamics (HD) and magnetohydrodynamics (MHD) scenarios. In both cases the asymptotic state and its dependence with both rotating and precession frequency was analyzed. For the MHD case no self-sustaining dynamos were found for the prograde precession case, whereas on the other hand a critical retrograde precession frequency was found above which dynamo action is self-sustained. It was also found that these correspond to small-scale dynamos with a developed turbulent regime. Furthermore, it is observed the presence of reversals of the magnetic dipole moment with greater waiting times between reversals for smaller precession frequencies.

In the present work, we study the energization and displacement of heavy ions through the use of test particles interacting with the electromagnetic fields of magnetohydrodynamic (MHD) turbulence. These fields are obtained from pseudospectral direct numerical solutions (DNSs) of the compressible three-dimensional MHD equations with a strong background magnetic field. We find particle energization to be predominantly perpendicular as the ions become heavier (lower charge-to-mass ratio) and that high displacement is detrimental for perpendicular energization. On the other hand, perpendicular displacement is unaffected by the charge-to-mass ratio, which we explain with a simple guide center model. Using Voronoi tessellation along with this model, we analyze preferential concentration and find that particles behave as tracers in the perpendicular plane, clustering in regions with $\nabla_\perp\cdot\mathbf{u}_\perp < 0$. These regions also have $(\nabla\times\mathbf{E})_z < 0$, which is optimal for perpendicular energization, thus providing a mechanism to understand precedent results.

Using direct numerical simulations (DNSs), the interaction between linear waves and turbulence under the compressible magnetohydrodynamic (CMHD) approach was studied. A set of DNSs in three dimensions for a spatial resolution of $128^3$ and $256^3$ were performed. A parametric study was carried out varying the sonic Mach number, the mean magnetic field and the compressibility amplitude of the forcing. Spatio-temporal spectra of the magnetic energy were built and analyzed, allowing for direct identification of all wave modes in a CMHD turbulent system and quantification of the amount of energy in each mode as a function of the wave number. Thus, linear waves were detected, that is Alfv\'en waves and fast and slow magnetosonic waves. Furthermore, different responses of the plasma were found according to whether the Mach number or the mean magnetic field was varied. On the other hand, making use of spatio-temporal spectra and two different integration methods, we accurately quantified the amount of energy present in each of the normal modes. Finally, although the presence of linear waves was observed, in all the cases studied the system was mainly dominated by the non-linear dynamics of the plasma., Comment: arXiv admin note: substantial text overlap with arXiv:1707.09190

A high-order method to evolve in time electromagnetic and velocity fields in conducting fluids with non-periodic boundaries is presented. The method has a small overhead compared with fast FFT-based pseudospectral methods in periodic domains. It uses the magnetic vector potential formulation for accurately enforcing the null divergence of the magnetic field, and allowing for different boundary conditions including perfectly conducting walls or vacuum surroundings, two cases relevant for many astrophysical, geophysical, and industrial flows. A spectral Fourier continuation method is used to accurately represent all fields and their spatial derivatives, allowing also for efficient solution of Poisson equations with different boundaries. A study of conducting flows at different Reynolds and Hartmann numbers, and with different boundary conditions, is presented to study convergence of the method and the accuracy of the solenoidal and boundary conditions.

We present a Fourier Continuation-based parallel pseudospectral method for incompressible fluids in cuboid non-periodic domains. The method produces dispersionless and dissipationless derivatives with fast spectral convergence inside the domain, and with very high order convergence at the boundaries. Incompressibility is imposed by solving a Poisson equation for the pressure. Being Fourier-based, the method allows for fast computation of spectral transforms. It is compatible with uniform grids (although refined or nested meshes can also be implemented), which in turn allows for explicit time integration at sufficiently high Reynolds numbers. Using a new parallel code named SPECTER we illustrate the method with two problems: channel flow, and plane Rayleigh-B\'enard convection under the Boussinesq approximation. In both cases the method yields results compatible with previous studies using other high-order numerical methods, with mild requirements on the time step for stability.

We study the spatio-temporal behavior of the Els\"asser variables describing magnetic and velocity field fluctuations, using direct numerical simulations of three-dimensional magnetohydrodynamic turbulence. We consider cases with relatively small, intermediate, and large values of a mean background magnetic field, and with null, small, and high cross-helicity (correlations between the velocity and the magnetic field). Wavenumber-dependent time correlation functions are computed for the different simulations. From these correlation functions, the decorrelation time is computed and compared with different theoretical characteristic times: the local non-linear time, the random-sweeping time, and the Alfv\'enic time. It is found that decorrelation times are dominated by sweeping effects for low values of the mean magnetic field and for low values of the cross-helicity, while for large values of the background field or of the cross-helicity and for wave vectors sufficiently aligned with the guide field, decorrelation times are controlled by Alfv\'enic effects. Finally, we observe counter-propagation of Alfv\'enic fluctuations due to reflections produced by inhomogeneities in the total magnetic field. This effect becomes more prominent in flows with large cross-helicity, strongly modifying the propagation of waves in turbulent magnetohydrodynamic flows., Comment: 16 pages, 40 figures

A parametric study of the magnetic dipole behavior in resistive incompressible MHD inside a rotating sphere is performed, using direct numerical simulations and considering Reynolds and Ekman numbers as controlling parameters. The tendency is to obtain geodynamo-like magnetic dipole reversal regimes for sufficiently small Ekman and large Reynolds numbers. The typical dipole latitude obtained in the reversal regime is around 40 degrees (with respect to the rotation axis of the sphere). A statistical analysis of waiting times between dipole reversals is also performed, obtaining a non-Poissonian distribution of waiting times, indicating long-term memory effects. We also report the presence of a $1/f$ frequency power spectrum in the magnetic dipole time-series, which also shows a tendency to grow toward lower frequencies as the Ekman number is decreased., Comment: 14 pages, 9 figures

Three-dimensional direct numerical simulations are used to study the energy cascade rate in isothermal compressible magnetohydrodynamic turbulence. Our analysis is guided by a two-point exact law derived recently for this problem in which flux, source, hybrid, and mixed terms are present. The relative importance of each term is studied for different initial subsonic Mach numbers $M_S$ and different magnetic guide fields ${\bf B}_0$. The dominant contribution to the energy cascade rate comes from the compressible flux, which depends weakly on the magnetic guide field ${\bf B}_0$, unlike the other terms whose modulus increase significantly with $M_S$ and ${\bf B}_0$. In particular, for strong ${\bf B}_0$ the source and hybrid terms are dominant at small scales with almost the same amplitude but with a different sign. A statistical analysis made with an isotropic decomposition based on the SO(3) rotation group is shown to generate spurious results in presence of ${\bf B}_0$, when compared with an axisymmetric decomposition better suited to the geometry of the problem. Our numerical results are compared with previous analyses made with in-situ measurements in the solar wind and the terrestrial magnetosheath.

Using spatio-temporal spectra we show direct evidence of excitation of magnetosonic and Alfv\'en waves in three-dimensional compressible magnetohydrodynamic turbulence at small Mach numbers. For the plasma pressure dominated regime, or high $\beta$ regime (with $\beta$ the ratio between fluid and magnetic pressure), and for the magnetic pressure dominated regime, or low $\beta$ regime, we study magnetic field fluctuations parallel and perpendicular to a guide magnetic field $\textbf{B}_0$. In the low $\beta$ case we find excitation of compressible and incompressible fluctuations, with a transfer of energy towards Alfv\'enic modes and to a lesser extent towards magnetosonic modes. In particular, we find signatures of the presence of fast magnetosonic waves in a scenario compatible with that of weak turbulence. In the high $\beta$ case, fast and slow magnetosonic waves are present, with no clear trace of Alfv\'en waves, and a significant part of the energy is carried by two-dimensional turbulent eddies.

The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of the Larmor radius of the charged particle to the characteristic outer length scale of the turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared with those from computer simulations, showing good agreement.

We derive the von K\'arm\'an-Howarth equation for a full three dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifth" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in-situ measurements in the solar wind at different spatial ranges.

We study the role of the Hall current and electron inertia in collisionless magnetic reconnection within the framework of full two-fluid MHD. At spatial scales smaller than the electron inertial length, a topological change of magnetic field lines exclusively due to electron inertia becomes possible. Assuming stationary conditions, we derive a theoretical scaling for the reconnection rate, which is simply proportional to the Hall parameter. Using a pseudo-spectral code with no dissipative effects, our numerical results confirm this theoretical scaling. In particular, for a sequence of different Hall parameter values, our numerical results show that the width of the current sheet is independent of the Hall parameter while its thickness is of the order of the electron inertial range, thus confirming that the stationary reconnection rate is proportional to the Hall parameter.

We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure and electron inertia. According to this description, each plasma species introduces a new spatial scale: the ion inertial length $\lambda_{i}$ and the electron inertial length $\lambda_{e}$, which are not present in the traditional MHD description. In the present paper, we seek for possible changes in the energy power spectrum in fully developed turbulent regimes, using numerical simulations of the two-fluid equations in two-and-a-half dimensions (2.5D). We have been able to reproduce different scaling laws in different spectral ranges, as it has been observed in the solar wind for the magnetic energy spectrum. At the smallest wavenumbers where plain MHD is valid, we obtain an inertial range following a Kolmogorov $k^{-5/3}$ law. For intermediate wavenumbers such that $\lambda_{i}^{-1} << k << \lambda_{e}^{-1}$, the spectrum is modified to a $k^{-7/3}$ power-law, as has also been obtained for Hall-MHD (HMHD) neglecting electron inertia terms. When electron inertia is retained, a new spectral region given by $k > \lambda_{e}^{-1}$ arises. The power spectrum for magnetic energy in this region is given by a $k^{-11/3}$ power law. Finally, when the terms of electron inertia are retained, we study the self-consistent electric field. Our results are discussed and compared with those obtained in solar wind observations and previous simulations.

We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von K\'arm\'an swirling flow between two counter-rotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field, and a case with self-sustained magnetic fields. Evidence of long-term memory and $1/f$ noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von K\'arm\'an flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large scale magnetic field., Comment: 10 pages, 9 figures

Much of the progress in our understanding of dynamo mechanisms has been made within the theoretical framework of magnetohydrodynamics (MHD). However, for sufficiently diffuse media, the Hall effect eventually becomes non-negligible. We present results from three dimensional simulations of the Hall-MHD equations subjected to random non-helical forcing. We study the role of the Hall effect in the dynamo efficiency for different values of the Hall parameter, using a pseudospectral code to achieve exponentially fast convergence. We also study energy transfer rates among spatial scales to determine the relative importance of the various nonlinear effects in the dynamo process and in the energy cascade. The Hall effect produces a reduction of the direct energy cascade at scales larger than the Hall scale, and therefore leads to smaller energy dissipation rates. Finally, we present results stemming from simulations at large magnetic Prandtl numbers, which is the relevant regime in hot and diffuse media such a the interstellar medium., Comment: 11 pages and 11 figures

The nonlinear dynamics of a bundle of magnetic flux ropes driven by stationary fluid motions at their endpoints is studied, by performing numerical simulations of the magnetohydrodynamic (MHD) equations. The development of MHD turbulence is shown, where the system reaches a state that is characterized by the ratio between the Alfven time (the time for incompressible MHD waves to travel along the field lines) and the convective time scale of the driving motions. This ratio of time scales determines the energy spectra and the relaxation toward different regimes ranging from weak to strong turbulence. A connection is made with phenomenological theories for the energy spectra in MHD turbulence., Comment: Published in Physics of Plasmas

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations, used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum $E_k\simeq k^{-3/2}$ and heating rate levels compatible with the heating requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfven time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model., Comment: 12 pages, 4 figures. Astrophysical Journal Letters (in press)

We perform direct numerical simulations of an externally driven two-dimensional magnetohydrodynamic system over extended periods of time to simulate the dynamics of a transverse section of a solar coronal loop. A stationary and large-scale magnetic forcing was imposed, to model the photospheric motions at the magnetic loop footpoints. A turbulent stationary regime is reached, which corresponds to energy dissipation rates consistent with the heating requirements of coronal loops. The temporal behavior of quantities such as the energy dissipation rate show clear indications of intermittency, which are exclusively due to the strong nonlinearity of the system. We tentatively associate these impulsive events of magnetic energy dissipation to the so-called nanoflares. A statistical analysis of these events yields a power law distribution as a function of their energies with a negative slope of 1.5, which is consistent with those obtained for flare energy distributions reported from X-ray observations., Comment: 12 pages, Latex (AASTeX), 3 figures, ApJ Lett (in press)