Related papers: High-speed shear driven dynamos. Part 2. Numerical…
This paper considers magnetic field generation by a fluid flow in a system referred to as the Archontis dynamo: a steady nonlinear magnetohydrodynamic (MHD) state is driven by a prescribed body force. The field and flow become almost equal…
We review works on the asymptotic stability of the Couette flow. The majority of the paper is aimed towards a wide range of applied mathematicians with an additional section aimed towards experts in the mathematical analysis of PDEs.
One method and two results are contributed to the complete understanding about MHD laminar flow in annular channel with transverse magnetic field in this paper. In terms of the method, a computationally cheap semi-analytic algorithm is…
This paper concerns the Couette flow for 2-D compressible Navier-Stokes equations (N-S) in an infinitely long flat torus $\Torus\times\R$. Compared to the incompressible flow, the compressible Couette flow has a stronger lift-up effect and…
We study the stability of the Couette flow $(y,0,0)^T$ in the 3D incompressible magnetohydrodynamic (MHD) equations for a conducting fluid on $\mathbb{T} \times \mathbb{R} \times \mathbb{T} $ in the presence of a homogeneous magnetic field…
In this paper we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum and total energy…
We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy $\Omega_o/\Omega_i=(r_o/r_i)^{-3/2}$. In this quasi-Keplerian regime a…
We present an exact analytic solution for decaying incompressible magnetohydrodynamic (MHD) turbulence. Our solution reveals a dual formulation in terms of two interacting Euler ensembles--one for hydrodynamic and another for magnetic…
Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfv\'{e}n waves, which interact and rapidly…
Many exact coherent states (ECS) arising in wall-bounded shear flows have an asymptotic structure at extreme Reynolds number Re in which the effective Reynolds number governing the streak and roll dynamics is O(1). Consequently, these…
In this paper, we study the existence of strong solutions to the two-phase magnetohydrodynamic equations in a bounded domain $\Omega\subseteq \mathbb{R}^3$. The fluids are incompressible, viscous, and resistive. The surface tension is…
A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging…
Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical…
It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled…
This is a brief review of the main results of our recent studies of the nonlinear evolution of the small-scale MHD dynamo in the high-Prandtl-number regime and of the structure of the resulting saturated state of the isotropic homogeneous…
Numerical simulations with self-similar initial and boundary conditions provide a link between theoretical and numerical investigations of jet dynamics. We perform axisymmetric resistive magnetohydrodynamic (MHD) simulations for a…
We investigate the linear stability of shears near the Couette flow for a class of 2D incompressible stably stratified fluids. Our main result consists of nearly optimal decay rates for perturbations of stationary states whose velocities…
In a previous paper, we have reported numerical simulations of the MHD flow driven by a travelling magnetic field (TMF) in an annular channel, at low Reynolds number. It was shown that the stalling of such induction pump is strongly related…
This paper is concerned with the asymptotic behaviors of global strong solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in two-dimensional periodic domains in…
This study examines the hydrodynamic and magnetohydrodynamic numerical solution of an electrically conducting fluid flow in a backward facing step (BFS) geometry under the influence of an external, uniform magnetic field applied at an…