Hydromagnetic Instability Research Articles

Tracking Hidden Magnetospheric Fluctuations in Accretion-powered Pulsars With a Kalman Filter

X-ray flux and pulse period fluctuations in an accretion-powered pulsar convey important information about the disk–magnetosphere interaction. It is shown that simultaneous flux and period measurements can be analysed with a Kalman filter based on the standard magnetocentrifugal accretion torque to generate accurate time-dependent estimates of three hidden state variables, which fluctuate stochastically and cannot be measured directly: the mass accretion rate, the Maxwell stress at the disk–magnetosphere boundary, and the radiative efficiency of accretion onto the stellar surface. The inferred fluctuation statistics carry implications for the physics of hydromagnetic instabilities at the disk–magnetosphere boundary and searches for continuous gravitational radiation from low-mass X-ray binaries.

A fully decoupled linearized finite element method with second-order temporal accuracy and unconditional energy stability for incompressible MHD equations

For highly coupled nonlinear incompressible magnetohydrodynamic (MHD) system, a well-known numerical challenge is how to establish an unconditionally energy stable linearized numerical scheme which also has a fully decoupled structure and second-order time accuracy. This paper simultaneously reaches all of these requirements for the first time by developing an effective numerical scheme, which combines a novel decoupling technique based on the “zero-energy-contribution” feature satisfied by the coupled nonlinear terms, the second-order projection method for dealing with the fluid momentum equations, and a finite element method for spatial discretization. The implementation of the scheme is very efficient, because only a few independent linear elliptic equations with constant coefficients need to be solved by the finite element method at each time step. The unconditional energy stability and well-posedness of the scheme are proved. Various 2D and 3D numerical simulations are carried out to illustrate the developed scheme, including convergence/stability tests and some benchmark MHD problems, such as the hydromagnetic Kelvin-Helmholtz instability, and driven cavity problems.

Hydromagnetic Instability of Two Viscoelastic Dusty-Fluids in Porous Medium

An attempt has been made to investigate the instability of the plane interface between two viscoelastic superposed conducting fluids in the presence of suspended particles and variable horizontal magnetic field through porous medium is studied. The cases of two fluids of uniform densities, viscosities, magnetic fields, and suspended particles number densities separated by a horizontal boundary; and of exponentially varying density, viscosity, suspended particles number density, and magnetic field are considered. It is found that the stability criterion is independent of the effects of viscoelasticity, medium porosity, and suspended particles but is dependent on the orientation and magnitude of the magnetic field. The magnetic field succeeds in stabilizing a certain range of wavenumbers which were unstable in the absence of the magnetic field. The system is found to be stable for potentially stable configuration/stratification. The growth rates are found to increase (for certain wavenumbers) and decrease (for other wavenumbers) with the increase in kinematic viscosity, suspended particles number density, magnetic field, medium permeability and stress relaxation time.

Hydromagnetic Instabilities in a Nonuniformly Rotating Layer of an Electrically Conducting Nanofluid

Hydromagnetic Instabilities in a Nonuniformly Rotating Layer of an Electrically Conducting Nanofluid

EFFECT OF AN APPLIED MAGNETIC FIELD AND GRAVITY MODULATION ON THE TIME DEPENDENT HYDRO-MAGNETIC INSTABILITY

In this present study a linear hydro-magnetic instability of time-dependent convection is designed and analyzed by using extended Stuart-Davis technique. The time variations are applied by fluctuating the fluid layer in the direction perpendicular to the flow and also the gravity modulation is introduced as sine and exponential function of time is considered to be one of the important effect. The extended Stuart-Davis technique is applied in tackling the time-dependency. To understand the effect of applied magnetic field and gravity modulation on the convection is analyzed with respect to different values of Chandrasekhar's number. The results shows that the magnetic field is having stabilizing impact in case of sinusoidal variation gravity field on the contrast it as destabilizing impact in case of exponential variation of gravity for short time but in long run it is having stabilizing effect.

Comparison of momentum transport models for numerical relativity

The main problems of nonvacuum numerical relativity, compact binary mergers and stellar collapse, involve hydromagnetic instabilities and turbulent flows, so that kinetic energy at small scales have mean effects at large scale that drive the secular evolution. Notable among these effects is momentum transport. We investigate two models of this transport effect, a relativistic Navier-Stokes system and a turbulent mean stress model, that are similar to all of the prescriptions that have been attempted to date for treating subgrid effects on binary neutron star mergers and their aftermath. Our investigation involves both stability analysis and numerical experimentation on star and disk systems. We also begin the investigation of the effects of particle and heat transport on post-merger simulations. We find that correct handling of turbulent heating can be important for avoiding unphysical instabilities. Given such appropriate handling, the evolution of a differentially rotating star and the accretion rate of a disk are reassuringly insensitive to the choice of prescription. However, disk outflows can be sensitive to the choice of method, even for the same effective viscous strength. We also consider the effects of eddy diffusion in the evolution of an accretion disk and show that it can interestingly affect the composition of outflows.

English

English

Hydromagnetic instability of a thin viscoelastic layer on a moving column

The issue of hydromagnetic instability for a viscoelastic condensate film streaming down on a normal moving cylinder is discussed. As the visco-elasticity, heat-transfer influence or the magnetic field are included into the governing equations, the results become more suitable with the real situation. The nonlinearity enhances the accuracy of the results. The flow stability is weakened by the reduction of the volume of cylinder. However, the response of the system due to the temperature difference is uncertain. Moreover, the increment of magnetic field can enhance the stability. In contrast to the linear-results, the flow can be stabilized by the rheology.

Convective hydromagnetic instabilities of a power-law liquid saturating a porous medium: Flux conditions

We investigate how an external imposed magnetic field affects thermal instability in a horizontal shallow porous cavity saturated by a non-Newtonian power-law liquid. The magnetic field is assumed to be constant and parallel to the gravity. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. We use linear stability analysis to find expressions for the critical Rayleigh number as a function of the power-law index and the intensity of the magnetic field. We use nonlinear parallel flow theory to find some explicit solutions of the problem, and we use finite difference numerical simulations to solve the full nonlinear equations. We show how the presence of magnetic field alters the known hydrodynamical result of Newtonian flows and power-law flows and how it causes the presence of subcritical finite amplitude convection for both pseudoplastic and dilatant fluids. We also show that in the limit of very strong magnetic field, the dissipation of energy by Joule effect dominates the dissipation of energy by shear stress and gives to the liquid an inviscid character.

Bipolar region formation in stratified two-layer turbulence

This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around $100$ across the turbulent layer. For the Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.

Subcritical excitation of the current-driven Tayler instability by super-rotation

It is known that in a hydrodynamic Taylor-Couette system, uniform rotation or a rotation law with positive shear (“super-rotation”) is linearly stable. It is also known that a conducting fluid under the presence of a sufficiently strong axial electric-current becomes unstable against nonaxisymmetric disturbances. It is thus suggestive that a cylindrical pinch formed by a homogeneous axial electric-current is stabilized by rotation laws with dΩ/dR ≥ 0. For magnetic Prandtl number Pm ≠ 1 and for slow rotation, however, rigid rotation and super-rotation support the instability by lowering the critical Hartmann numbers. This double-diffusive instability of super-rotation even exists for toroidal magnetic fields with rather arbitrary radial profiles, the current-free profile Bϕ ∝ 1/R included. The sign of the azimuthal drift of the nonaxisymmetric hydromagnetic instability pattern strongly depends on the magnetic Prandtl number. The pattern counterrotates with the flow for Pm ≪ 1 and it corotates for Pm ≫ 1 while for rotation laws with negative shear, the instability pattern migrates in the direction of the basic rotation for all Pm. An axial electric-current of minimal 3.6 kA flowing inside or outside the inner cylinder suffices to realize the double-diffusive instability for super-rotation in experiments using liquid sodium as the conducting fluid between the rotating cylinders. The limit is 11 kA if a gallium alloy is used.

Alfven Wave Instabilities Related with Excess Charge as a Source of Jovian Magnetospheric Micropulsations

Hydromagnetic wave instabilities (Alfven wave instabilities, the physical picture of this instability is given in terms of wave-wave interaction) excited by an electron or ion beam passing through IO tours in the Jovian magnetosphere has been studied in the case of low wave frequency and small wave number in the presence of excess charge in the media. It has been obtained that the excess charge near IO has the dominant role in modifying the Alfvan wave instabilities in comparison to the other parameters. The central frequency of this instability is lying within the range of micropulsations for the presence of excess charge of 10-3 times the ambient plasma in the Jovian magnetosphere. Hence this excited Alfvan wave instabilities is the one of the possible generation mechanism for the micro-pulsations recorded by Voyager 1 and 2 in the Jovian Magnetosphere.

Hydromagnetic thermosolutal instability of Rivlin-Ericksen rotating fluid permeated with suspended particles and variable gravity field in porous medium

Abstract The thermosolutal instability of Rivlin-Ericksen elasticoviscous rotating fluid permeated with suspended particles (fine dust) and variable gravity field in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation and stable solute gradient has stabilizing effects and suspended particles are found to have destabilizing effect on the system whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions. The effect of rotation, suspended particles, magnetic field, stable solute gradient and medium permeability has also been shown graphically.

Saturation of nonaxisymmetric instabilities of magnetized spherical Couette flow.

We numerically investigate the saturation of the hydromagnetic instabilities of a magnetized spherical Couette flow. Previous simulations demonstrated a region where the axisymmetric flow, calculated from a 2D simulation, was linearly unstable to nonaxisymmetric perturbations. Full, nonlinear, 3d simulations showed that the saturated state would consist only of harmonics of one azimuthal wave number, though there were bifurcations and transitions as nondimensional parameters (Re, Ha) were varied. Here, the energy transfer between different azimuthal modes is formulated as a network. This demonstrates a mechanism for the saturation of one mode and for the suppression of other unstable modes. A given mode grows by extracting energy from the axisymmetric flow, and then saturates as the energy transfer to its second harmonic equals this inflow. At the same time, this mode suppresses other unstable modes by facilitating an energy transfer to linearly stable modes.

Hydromagnetic thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles in porous medium

Abstract In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions

Air-Aided Shear on a Thin Film Subjected to a Transverse Magnetic Field of Constant Strength: Stability and Dynamics

The effect of air shear on the hydromagnetic instability is studied through (i) linear stability, (ii) weakly nonlinear theory, (iii) sideband stability of the filtered wave, and (iv) numerical integration of the nonlinear equation. Additionally, a discussion on the equilibria of a truncated bimodal dynamical system is performed. While the linear and weakly nonlinear analyses demonstrate the stabilizing (destabilizing) tendency of the uphill (downhill) shear, the numerics confirm the stability predictions. They show that (a) the downhill shear destabilizes the flow, (b) the time taken for the amplitudes corresponding to the uphill shear to be dominated by the one corresponding to the zero shear increases with magnetic fields strength, and (c) among the uphill shear-induced flows, it takes a long time for the wave amplitude corresponding to small shear values to become smaller than the one corresponding to large shear values when the magnetic field intensity increases. Simulations show that the streamwise and transverse velocities increase when the downhill shear acts in favor of inertial force to destabilize the flow mechanism. However, the uphill shear acts oppositely. It supports the hydrostatic pressure and magnetic field in enhancing films stability. Consequently, reduced constant flow rates and uniform velocities are observed.

Analysis of global hydromagnetic instabilities driven by strongly sheared toroidal flows in tokamak plasmas

Recent numerical calculations have shown that while strong toroidal rotation can increase the external kink limit of tokamak plasmas, the associated rotation shear can drive a Kelvin–Helmholtz like global instability in the plasma, if the rotation frequency exceeds a threshold value (Chapman et al 2011 Plasma Phys. Control. Fusion 53 125002; Chapman et al 2012 Nucl. Fusion 52 042005). On the basis of a large aspect ratio toroidal expansion of the magnetohydrodynamic stability equations, the present paper investigates analytically various properties of this instability in tokamak plasmas with sonic toroidal flows and low magnetic shear in the core region. We also compare the analytical results with numerical code calculations. Many characteristic features and parameter dependences of the instability can be understood from the analytical theory, such as an eigenmode structure peaking at the position of largest rotation shear, and insensitivity of the growth rate to the plasma beta and to the precise value of the safety factor in the region of low magnetic shear. From an algebraic expression for the growth rate, valid asymptotically at large rotation frequencies, the drop in the dynamic pressure associated with the flow in the plasma can be identified as a major driving mechanism of the instability. For modes with (dominant) poloidal mode number m > 1, and rotating equilibria with isothermal magnetic surfaces, another driving mechanism of the instability is related to the centrifugally induced density variation along the magnetic field lines.

Study on hydro-magnetic capillary instability with mass transfer through porous media

The linear analysis of hydro-magnetic capillary instability of a cylindrical interface between two viscous and magnetic fluids in a fully saturated porous medium has been carried out, when the fluids are subjected to a constant axial magnetic field and, when there is heat and mass transfer across the interface. The viscous potential flow theory has been used for the investigation. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied magnetic field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as magnetic field strength, heat transfer capillary number, vapour fraction, permeability and porosity on the stability of the system. It has been observed that heat transfer and magnetic field both have stabilizing effect while porosity has destabilizing effect on the stability of the system.

Are gravitational waves from giant magnetar flares observable?

Are giant flares in magnetars viable sources of gravitational radiation? Few theoretical studies have been concerned with this problem, with the small number using either highly idealized models or assuming a magnetic field orders of magnitude beyond what is supported by observations. We perform nonlinear general-relativistic magnetohydrodynamics simulations of large-scale hydromagnetic instabilities in magnetar models. We utilise these models to find gravitational wave emissions over a wide range of energies, from 10^40 to 10^47 erg. This allows us to derive a systematic relationship between the surface field strength and the gravitational wave strain, which we find to be highly nonlinear. In particular, for typical magnetar fields of a few times 10^15 G, we conclude that a direct observation of f-modes excited by global magnetic field reconfigurations is unlikely with present or near-future gravitational wave observatories, though we also discuss the possibility that modes in a low-frequency band up to 100 Hz could be sufficiently excited to be relevant for observation.

Hydromagnetic thermosolutal instability of compressible walters' (model B') rotating fluid permeated with suspended particles in porous medium

The thermosolutal instability of compressible Walters' (model B') elastico-viscous rotating fluid permeated with suspended particles (fine dust) in the presence of vertical magnetic field in porous medium is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection the Walters' (model B') fluid behaves like an ordinary Newtonian fluid and it is observed that the rotation and stable solute gradient has stabilizing effects and suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions.