Related papers: Resistive instabilities in sinusoidal shear flows …
Inspired by the experiment from Moresco \& Alboussi\`ere (2004, J. Fluid Mech.), we study the stability of a liquid metal flow in a rectangular, electrically insulating duct with a steady homogeneous transverse magnetic field. The Lorentz…
This paper is concerned with the vanishing viscosity and magnetic resistivity limit for the two-dimensional steady incompressible MHD system on the half plane with no-slip boundary condition on velocity field and perfectly conducting wall…
I shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertia-less flows with curved streamlines. Then I describe a theory of elastic turbulence and prediction of elastic waves at…
Using a 2D Viscoresistive Reduced MagnetoHydroDynamic (VR-RMHD) model, the magnetic island coalescence problem is studied in the presence of in-plane, parallel shear flows. Extending the analytical work of Waelbroeck et al [33] and…
In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where the magnetic field is vertical. More precisely, by exploiting…
It is well established now that the solar atmosphere, from photosphere to the corona and the solar wind is a highly structured medium. Satellite observations have confirmed the presence of steady flows. Here, we investigate the parallel…
In this work we introduce a novel semi-implicit structure-preserving finite-volume/finite-difference scheme for the viscous and resistive equations of magnetohydrodynamics (MHD) based on an appropriate 3-split of the governing PDE system,…
This study is concerned with numerical linear stability analysis of liquid metal flow in a square duct with thin electrically conducting walls subject to a uniform transverse magnetic field. We derive an asymptotic solution for the base…
In this article we consider the stability threshold of the 2D magnetohydrodynamics (MHD) equations near a combination of Couette flow and large constant magnetic field. We study the partial dissipation regime with full viscous and only…
A self-consistent, thermodynamic approach is employed to derive the wave energy of a magnetohydrodynamic system within the harmonic approximation and to obtain the familiar dispersion relation from the resulting equation of motion. The…
We present a symmetry classification of the linearised Navier-Stokes equations for a two-dimensional unbounded linear shear flow of an incompressible fluid. The full set of symmetries is employed to systematically derive invariant ansatz…
We study magnetic Taylor-Couette flow in a system having nondimensional radii $r_i=1$ and $r_o=2$, and periodic in the axial direction with wavelengths $h\ge100$. The rotation ratio of the inner and outer cylinders is adjusted to be…
We study the magneto-rotational instability of an incompressible flow which rotates with angular velocity Omega(r)=a+b/r^2 where r is the radius and $a$ and b are constants. We find that an applied magnetic field destabilises the flow, in…
We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity) and threaded by a…
Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic…
Three eigenvalue bounds are derived for the instability of ideal compressible stratified magnetohydrodynamic shear flows in which the base velocity, density, and magnetic field vary in two directions. The first bound can be obtained by…
We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to $4096^2$, for which several quadratic invariants are preserved by the truncation and…
This paper investigates the non-linear dynamics of horizontal shear instability in an incompressible, stratified and rotating fluid in the non-traditional $f$-plane, i.e. with the full Coriolis acceleration, using direct numerical…
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic…
First, we consider Kolmogorov flow (a shear flow with a sinusoidal velocity profile) for 2D Navier-Stokes equation on a torus. Such flows, also called bar states, have been numerically observed as one type of metastable states in the study…