Spectral Properties of MHD Turbulence in 2.5-Dimensional Compressible Plasmas

Spectral properties of magnetohydrodynamic （MHD） turbulence with a strong back- ground mean magnetic field in 2.5-dimensional compressible plasmas are studied by high-resolution numerical simulations. The spatial properties of MHD turbulences and the energy transfer process in the k-space are analyzed through angle-averaged energy spectrum. It is found that in the inertial phase, the energy spectrum index of compressible MHD turbulences during the decaying phase is evolved with time. The index varies in a quite wide regime from Kolmogorov＇s 5/3 to IK＇s 3/2 during the late simulation period. The energy spectrum index in the later nonlinear stage is also dependent on the chosen initial conditions. The spectral index increases with the increase of the initial magnetic fluctuation while the index decreases with the increase of the initial flow perturbation.

Invariants in Relativistic MHD Turbulence

The objective of this work is to understand how the characteristics of relativistic MHD turbulence may differ from those of nonrelativistic MHD turbulence. We accomplish this by studying the ideal invariants in the relativistic case and comparing them to what we know of nonrelativistic turbulence. Although much work has been done to understand the dynamics of nonrelativistic systems (mostly for ideal incompressible fluids), there is minimal literature explicitly describing the dynamics of relativistic MHD turbulence using numerical simulations. Many researchers simply assume that relativistic turbulence has the same invariants and obeys the same dynamics as non-relativistic systems. Our results show that this assumption may be incorrect.

Low Rm MHD Turbulence:The Role of Boundaries

In this Keynote lecture,we review the main known features of MHD turbulence at low magnetic Reynolds number,that is when the flow isn't intense enough to disturb an externally applied magnetic field.The emphasis is deliberately placed on the very specific physical mechanisms of this type of flows,rather than their numerical modelling. We also focus on homogeneous magnetic fields which have received most attention.We stress in particular that the tendency to two-dimensionality observed in these flows casts the boundaries of the domain into a leading role.

LSFEM Implementation of MHD Numerical Solver

Many problems in physics are inherently of multi-scale nature. The issues of MHD turbulence or magnetic reconnection, namely in the hot and sparse, almost collision-less astrophysical plasmas, can stand as clear examples. The Finite Element Method (FEM) with adaptive gridding appears to be the appropriate numerical implementation for handling the broad range of scales contained in such high Lundquist-number MHD problems. In spite the FEM is now routinely used in engineering practice in solid-state and fluid dynamics, its usage for MHD simulations has recently only begun and only few implementations exist so far. In this paper we present our MHD solver based on the Least-Square FEM (LSFEM) formulation. We describe the transformation of the MHD equations into form required for finding the LSFEM functional and some practical issues in implementation of the method. The algorithm was tested on selected problems of ideal (non-resistive) and resistive MHD. The tests show the usability of LSFEM for solving MHD equations.

Analysis of the instability growth rate during the jet-background interaction in a magnetic field

The two-stream instability is common, responsible for many observed phe- nomena in nature, especially the interaction of jets of various origins with the back- ground plasma （e.g. extragalactic jet interacting with the cosmic background）. The dispersion relation that does not consider magnetic fields is described by the well- known Buneman relation. In 2011, Bohata, Bren and Kulhanek derived the relation for the two-stream instability without the cold limit, with the general orientation of a magnetic field, and arbitrary stream directions. The maximum value of the imaginary part of the individual dispersion branches ωn（k） is of interest from a physical point of view. It represents the instability growth rate which is responsible for the onset of turbulence mode and subsequent reconnection on the scale of the ion radius accom- panied by a strong plasma thermalization. The paper presented here is focused on the non-relativistic instability growth rate and its dependence on various input parameters, such as magnitude and direction of magnetic field, sound velocity, plasma frequency of the jet and direction of the wave vector during the jet - intergalactic medium in- teraction. The results are presented in plots and can be used for determination of the plasma parameter values close to which the strong energy transfer and thermalization between the jet and the background plasma occur.

Numerical Modeling of Turbulent Melt Flow in a Continuous Casting Mold Affected by an Electromagnetic Brake

The current work combines numerical and experimental investigations based on a small-scale mockup using the eutectic alloy GaInSn.The jet flow discharging from the submerged entry nozzle was exposed perpendicularly to a DC magnetic field across the entire wide face of the mold.Numerical calculations were performed by using the commercial package CFX with an implemented RANS-SST turbulence model.The anisotropic properties of the MHD turbulence were taken into account by specific modifications of the turbulence model.The comparison between our numerical calculations and the experimental results shows a very well agreement.In particular,the modified RANS-SST turbulence model is capable to reconstruct the peculiar phenomenon of the excitation of non-steady,non-isotropic large-scale flow perturbations caused by the application of the DC magnetic field.Another important finding of our study is the feature that the electrical boundary conditions,namely the wall conductivity ratio,have a great impact on the mold flow subjected to an external magnetic field.