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Register a new userSpatio-temporal behavior of magnetohydrodynamic fluctuations with cross-helicity and background magnetic field
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We study the spatio-temporal behavior of the Elsasser 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 Alfvenic 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 Alfvenic effects. Finally, we observe counter-propagation of Alfvenic 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.
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Using direct numerical simulations of three-dimensional magnetohydrodynamic (MHD) turbulence the spatio-temporal behavior of magnetic field fluctuations is analyzed. Cases with relatively small, medium and large values of a mean background magnetic field are considered. The (wavenumber) scale dependent time correlation function is directly computed for different simulations, varying the mean magnetic field value. From this correlation function the time decorrelation is computed and compared with different theoretical times, namely, the local non-linear time, the random sweeping time, and the Alfvenic time, the latter being a wave effect. It is observed that time decorrelations are dominated by sweeping effects, and only at large values of the mean magnetic field and for wave vectors mainly aligned with this field time decorrelations are controlled by Alfvenic effects.
Energy dissipation is highly intermittent in turbulent plasmas, being localized in coherent structures such as current sheets. The statistical analysis of spatial dissipative structures is an effective approach to studying turbulence. In this paper, we generalize this methodology to investigate four-dimensional spatiotemporal structures, i.e., dissipative processes representing sets of interacting coherent structures, which correspond to flares in astrophysical systems. We develop methods for identifying and characterizing these processes, and then perform a statistical analysis of dissipative processes in numerical simulations of driven magnetohydrodynamic turbulence. We find that processes are often highly complex, long-lived, and weakly asymmetric in time. They exhibit robust power-law probability distributions and scaling relations, including a distribution of dissipated energy with power-law index near -1.75, indicating that intense dissipative events dominate the overall energy dissipation. We compare our results with the previously observed statistical properties of solar flares.
Magnetic helicity is robustly conserved in systems with large magnetic Reynolds numbers, including most systems of astrophysical interest. This plays a major role in suppressing the kinematic large scale dynamo and driving the large scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. Errors in the internal distribution of magnetic helicity are equally serious and possibly larger. Here we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations.
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain models and is also supported by numerical studies of a variety of examples. In this paper we analyze the long-time behavior of a particular class of decoherent quantum walks, which, to the best of our knowledge, was only studied at the level of numerical simulations before. We consider a local coin operation which is randomly and independently chosen for each time step and each lattice site and prove that, under rather mild conditions, this leads to classical behavior: With the same scaling as needed for a classical diffusion the position distribution converges to a Gaussian, which is independent of the initial state. Our method is based on non-degenerate perturbation theory and yields an explicit expression for the covariance matrix of the asymptotic Gaussian in terms of the randomness parameters.
The rich structure that we observe in molecular clouds is due to the interplay between strong magnetic fields and supersonic (turbulent) velocity fluctuations. The velocity fluctuations interact with the magnetic field, causing it too to fluctuate. Using numerical simulations, we explore the nature of such magnetic field fluctuations, $vec{delta B}$, over a wide range of turbulent Mach numbers, $mathcal{M} = 2 - 20$ (i.e., from weak to strong compressibility), and Alfven Mach numbers, $mathcal{M}_{text{A}0} = 0.1 - 100$ (i.e., from strong to weak magnetic mean fields, $B_0$). We derive a compressible quasi-static fluctuation model from the magnetohydrodynamical (MHD) equations and show that velocity gradients parallel to the mean magnetic field give rise to compressible modes in sub-Alfvenic flows, which prevents the flow from becoming two-dimensional, as is the case in incompressible MHD turbulence. We then generalise an analytical model for the magnitude of the magnetic fluctuations to include $mathcal{M}$, and find $|vec{delta B}| = delta B = c_ssqrt{pirho_0}mathcal{M}mathcal{M}_{text{A}0}$, where $c_s$ is the sound speed and $rho_0$ is the mean density of gas. This new relation fits well in the strong $B$-field regime. We go on to study the anisotropy between the perpendicular ($ B_{perp}$) and parallel ($ B_{parallel}$) fluctuations and the mean-normalised fluctuations, which we find follow universal scaling relations, invariant of $mathcal{M}$. We provide a detailed analysis of the morphology for the $delta B_{perp}$ and $delta B_{parallel}$ probability density functions and find that eddies aligned with $B_0$ cause parallel fluctuations that reduce $B_{parallel}$ in the most anisotropic simulations. We discuss broadly the implications of our fluctuation models for magnetised gases in the interstellar medium.
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