Related papers: Small scales and anisotropy in low $Rm$ magnetohyd…
Steady Low $R_m$ MHD turbulence is investigated here through estimates of upper bounds for attractor dimension. A flow between two parallel walls with an imposed perpendicular magnetic field is considered. The flow is defined by its maximum…
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…
We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls, in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well…
We accomplish two major tasks. First, we show that the turbulent motion at large scales obeys Gaussian statistics in the interval 0 < Rlambda < 8.8, where Rlambda is the microscale Reynolds number, and that the Gaussian flow breaks down to…
This study is concerned with how the attractor dimension of the two-dimensional Navier--Stokes equations depends on characteristic length scales, including the system integral length scale, the forcing length scale, and the dissipation…
The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian,…
We investigate using direct numerical simulations with grids up to 1536^3 points, the rate at which small scales develop in a decaying three-dimensional MHD flow both for deterministic and random initial conditions. Parallel current and…
We derive upper bounds for the number of degrees of freedom of two-dimensional Navier--Stokes turbulence freely decaying from a smooth initial vorticity field $\omega(x,y,0)=\omega_0$. This number, denoted by $N$, is defined as the minimum…
We present Direct Numerical Simulations of decaying Magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number. The domain considered is bounded by periodic boundary conditions in the two directions perpendicular to the magnetic…
When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the…
This study seeks to elucidate the linear transient growth mechanisms in a uniform duct with square cross-section applicable to flows of electrically conducting fluids under the influence of an external magnetic field. A particular focus is…
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.…
The three-dimensional Navier-Stokes-$\alpha$ model for fast rotating geophysical fluids is considered. The Navier-Stokes-$\alpha$ model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian…
We present a new analysis of the anisotropic spectral energy distribution in incompressible magnetohydrodynamic (MHD) turbulence permeated by a strong mean magnetic field. The turbulent flow is generated by high-resolution pseudo-spectral…
We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high beta) and magnetically dominated (low beta) plasmas at different…
In this work we derive a lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing and for…
This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…
A method is proposed for computing coefficients in the Kazantsev equation of small-scale dynamo for the full spectrum of hydromagnetic turbulence comprising the inertial range together with the range of viscous dissipation. The dynamo…
This manuscript has been accepted for publication in Physical Review Fluids, see https://journals.aps.org/prfluids/accepted/d5074S28J6b11905012b7cb06505e8f2149dd5f20. This work investigates the mechanisms that underlie transitions to…
Deep autoencoder neural networks can generate highly accurate, low-order representations of turbulence. We design a new family of autoencoders which are a combination of a 'dense-block' encoder-decoder structure (Page et al, J. Fluid Mech.…