Related papers: D-dimensional developed MHD turbulence: Double exp…
Magnetohydrodynamic (MHD) turbulence in the majority of natural systems, including the interstellar medium, the solar corona, and the solar wind, has Reynolds numbers far exceeding the Reynolds numbers achievable in numerical experiments.…
A self-consistent renormalization (RG) scheme has been applied to nonhelical magnetohydrodynamic turbulence with normalized cross helicity $\sigma_c =0$ and $\sigma_c \to 1$. Kolmogorov's 5/3 powerlaw is assumed in order to compute the…
We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are,…
Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD) turbulence without and with mean magnetic field are analyzed by higher-order two-point statistics. The turbulence exhibits statistical anisotropy with respect to…
Within the framework of the renormalization group approach in the stochastic model of fully developed turbulence, the $\beta$-function has been calculated in the fourth order of perturbation theory for high-dimensional spaces $d \rightarrow…
We present a two-loop field-theoretic analysis of incompressible helical magnetohydrodynamics (MHD) in fully developed stationary turbulence. A key feature of helical MHD is the appearance of an infrared-unstable ``mass-like'' term in the…
The complete analysis of a model with three quartic coupling constants associated with an O(2N)--symmetric, a cubic, and a tetragonal interactions is carried out within the three-loop approximation of the renormalization-group (RG) approach…
We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stems from numerical simulations of decaying three-dimensional (3D)…
We study decaying magnetohydrodynamics (MHD) turbulence stemming from the evolution of the Taylor-Green (TG) flow generalized recently to MHD, with equal viscosity and magnetic resistivity and up to equivalent grid resolutions of 2048^3…
The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the…
An improved $\eps$ expansion in the $d$-dimensional ($d > 2$) stochastic theory of turbulence is constructed at two-loop order which incorporates the effect of pole singularities at $d \to 2$ in coefficients of the $\eps$ expansion of…
This paper concerns the stability of Kolmogorov flow u = (0, sin x) in the infinite (x,y)-plane. A mean magnetic field of strength B0 is introduced and the MHD linear stability problem studied for modes with wave-number k in the…
We present a detailed study of localised magnetohydrodynamical (MHD) instabilities occuring in two--dimensional magnetized accretion disks. We model axisymmetric MHD disk tori, and solve the equations governing a two--dimensional magnetized…
We present 3D magnetohydrodynamic (MHD) numerical simulations of the evolution of self--gravitating and weakly magnetized disks with an adiabatic equation of state. Such disks are subject to the development of both the magnetorotational and…
The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state…
We present a detailed direct numerical simulation of statistically steady, homogeneous, isotropic, two-dimensional magnetohydrodynamic (2D MHD) turbulence. Our study concentrates on the inverse cascade of the magnetic vector potential. We…
In this paper, we study the well-posedness of the Kolmogorov two-equation model of turbulence in a periodic domain $\mathbb{T}^d$, for space dimensions $d=2,3$. We admit the average turbulent kinetic energy $k$ to vanish in part of the…
In this paper, we establish the global well-posedness of the incompressible magnetohydrodynamics (MHD) system on $n-$dimensional $(n\geq 2)$ periodic boxes with either no magnetic diffusivity (non-resistive case) or no fluid viscosity…
Using a new numerical code we have carried out two-dimensional simulations of the nonlinear evolution of unstable sheared magnetohydrodynamic flows. We considered two cases: a strong magnetic field (Alfven Mach number, M_a = 2.5) and a weak…
The aim of the present work is to derive rigorous estimates for turbulent MHD flow quantities such as the size and anisotropy of the dissipative scales, as well as the transition between 2D and 3D state. To this end, we calculate an upper…