Related papers: Local Axisymmetric Diffusive Stability of Weakly-M…
In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be…
The spectral stability of liquid metal differentially rotating in transverse magnetic field is studied numerically by solving the eigenvalue problem with rigid-wall boundary conditions. The equilibrium velocity profile used in calculations…
Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the…
We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…
The linear stability of a shear-thinning, viscoelastic fluid undergoing any of the canonical rectilinear shear flows, viz., plane Couette flow and pressure-driven flow through a channel or a tube is analyzed in the creeping-flow limit using…
This manuscript has been accepted for publication in Physical Review Fluids, see https://journals.aps.org/prfluids/accepted/53075Se8O0b1b109b1cc0061b280aaa122f0f92dc. The stability of a pulsatile quasi-two-dimensional duct flow was…
It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal…
The quest for an unambiguous detection of magnetorotational instability (MRI) in experiments is still ongoing despite recent promising results. To conclusively identify MRI in the laboratory, a large cylindrical Taylor-Couette experiment…
The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered…
Decades ago S. Lundquist, S. Chandrasekhar, P.H. Roberts and R. J.~Tayler first posed questions about the stability of Taylor-Couette flows of conducting material under the influence of large-scale magnetic fields. These and many new…
We investigate the stabilizing effects of the magnetic fields in the linearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneous incompressible viscous magnetohydrodynamic fluid of zero resistivity in the presence of a uniform…
Symmetries and conservation laws associated with the ideal Einstein-Euler system, for stationary and axisymmetric stars, can be utilized to define a set of flow constants. These quantities are conserved along flow lines in the sense that…
The questions of how strong magnetic fields can be stored in rotating stellar radiative zones without being subjected to pinch-type instabilities and how much radial mixing is produced if the fields are unstable are addressed. Linear…
Fluid instabilities arise in a variety of contexts and are often unwanted results of engineering imperfections. In one particular model for a magnetized target fusion reactor, a pressure wave is propagated in a cylindrical annulus comprised…
We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionised accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of…
The variational principle for linear stability of three-dimensional, inhomogenious, compressible, moving magnetized plasma is suggested. The principle is ``softer'' (easier to be satisfied) than all previously known variational stability…
The stabilization of ``rigid'' flute and ballooning modes $m = 1$ in an axisymmetric mirror trap with the help of an ideally conducting lateral both in the presence and in the absence of end MHD anchors is studied. The calculations were…
The question is addressed whether stellar differentially rotating radiative zones (like the solar tachocline) excite nonaxisymmetric r-modes which can be observed. To this end the hydrodynamical stability of latitudinal differential…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
This paper is the first in a series investigating magnetohydrodynamic instabilities that may contribute to angular-momentum transport and magnetic-field evolution in stellar radiative zones. We focus on shear-driven instabilities,…