Rayleigh-Taylor instability of magnetized partially-ionized superposed fluids with rotation and surface tension in porous medium

The Rayleigh-Taylor instability of the plane interface separating the two partially-ionized superposed fluids through porous medium is analysed. The effect of variable horizontal magnetic field, surface tension and rotation along the vertical axis are also incorporated. The relevant linearized perturbation equations are taken and using normal mode analysis the general relation is obtained from which the dispersion relation for two superposed fluids of different densities is derived. It is found that the surface tension and horizontal magnetic field have the stabilizing effect on the R-T-instability. The condition of instability remains unaffected by the permeability of porous medium, presence of neutral particles in the fluids and rotation.It is concluded that the system is unstable only for those positive wave numbers which are less than certain critical value in case of an adverse density gradient.     

Effect of Hall Current and Finite Larmor Radius Corrections on Thermal Instability of Radiative Plasma for Star Formation in Interstellar Medium (ISM)

The effects of finite ion Larmor radius (FLR) corrections, Hall current and radiative heat-loss function on the thermal instability of an infinite homogeneous, viscous plasma incorporating the effects of finite electrical resistivity, thermal conductivity and permeability for star formation in interstellar medium have been investigated. A general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. The wave propagation is discussed for longitudinal and transverse directions to the external magnetic field and the conditions of modified thermal instabilities and stabilities are discussed in different cases. We find that the thermal instability criterion gets modified into radiative instability criterion. The finite electrical resistivity removes the effect of magnetic field and the viscosity of the medium removes the effect of FLR from the condition of radiative instability. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. Numerical calculation shows stabilizing effect of viscosity, heat-loss function and FLR corrections, and destabilizing effect of finite resistivity and permeability on the thermal instability. The outcome of the problem discussed the formation of star in the interstellar medium.     

Effect of rotation on magnetogravitational instability of finite conducting gas in presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetised gas-particle medium in the presence of suspended particles is investigated. The conductivity of the medium is assumed to be finite. The equations of the problem are linearized and the general dispersion relation is obtained. The rotation is assumed along two different directions separately and separate dispersion relation for each case is obtained. The dispersion relation for propagation parallel and perpendicular to the uniform magnetic field along with rotation is derived. It is found that in presence of suspended particles, magnetic field, finite conductivity, rotation and viscosity, Jeans's criterion determines the condition of gravitational instability of gas-particle medium.     

Effect of rotation and finite Larmor radius on magneto-gravitational instability of Hall plasma in the presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetized Hall plasma is considered with the inclusion of finite Larmor radius corrections and the effect of suspended particles. A general dispersion relation is obtained from the linearized set of equations. The particular cases of the effect of rotation along and perpendicular to the direction of the magnetic field are considered. The effects of Hall current, finite Larmor radius, and suspended particles on the waves propagated parallel and perpendicular to the uniform magnetic field are investigated along with the uniform rotation of the medium. It is found that in the presence of suspended particles, magnetic field, Hall current, rotation and finite Larmor radius, the Jeans criterion determines the condition of gravitational instability of a gas-particle medium.     

Kelvin-Helmholtz instability of superposed hydromagnetic fluids of different densities with finite-resistivity

The hydromagnetic Kelvin-Helmholtz instability of two superposed fluids of different densities is studied. One of the fluids is assumed to be static with finite-resistivity and another fluid is streaming and nonconducting. The equations of the problem are linearized and the dispersion relation using relevant boundary conditions has been derived. It is found that the ratio of densities of the fluids () modifies the condition of ideal-plasma modes. The influence of on stable and unstable regions as compared to the case when is unity has been investigated and illustrated. Further, the combined effect of small finite-resistivity and different densities of the fluids is analyzed. It has been found that merely changes the constant of proportionality of the growth rate, which is obtained for the fluids of the same densities.     

Finite larmor-radius effects on Rayleigh-Taylor instability of a dusty magnetized plasma

This paper discusses the Rayleigh-Taylor (RT) instability of an infinitely conducting medium having an exponential density distribution which includes the effects of finite ion Larmor-radius (FLR) corrections and suspended particles in the presence of a uniform horizontal magnetic field. The relevant equations of the problem are linearized and from the linearized perturbation equations a dispersion relation is obtained, using appropriate boundary conditions. It has been found that the criterion for the stable density stratification remains uninfluenced by the simultaneous inclusion of the FLR corrections and suspended particles. The stability of the medium has been proved for the case of stable stratification when the FLR corrections are not considered in the analysis. The growth rate of unstable RT modes with increasing relaxation frequency of the suspended particles is evaluated analytically. It has been shown that the presence of suspended particles in the medium suppresses the growth rate of the unstable RT modes, thereby implying a stabilizing influence of the particles on the considered configuration.     

Magneto-gravitational instability of a rotating and finitely-conducting fluid

The gravitational instability of an infinite homogeneous finitely conducting viscid fluid through porous medium is studied in the presence of a uniform vertical magnetic field and finite ion Larmor radius (FLR) effects. The medium is considered uniformly rotating along and perpendicular to the direction of the prevalent magnetic field. A general dispersion relation is obtained from the relevant linearized perturbation equations of the problem. Furthermore, the wave propagation along and perpendicular to the direction of existing magnetic field has been discussed for each direction of the rotation. It is found that the simultaneous presence of viscosity finite conductivity, rotation, medium porosity, and FLR corrections does not essentially change the Jeans's instability condition. The stabilizing influence of FLR in the case of transverse propagation is reasserted for a non-rotating and inviscid porous medium. It is shown that the finite conductivity has destabilizing influence on the transverse wave propagation whereas for longitudinal propagation finite conductivity does not affect the Jean's criterion.     

Rayleigh-Taylor instability of rotating fluid in the presence of a vertical magnetic field

The Rayleigh-Taylor instability of two rotating superposed fluids in the presence of a vertical magnetic field has been investigated. It is shown thatn ² is purely real, wheren is the growth rate of a perturbation. In the basis of this fact it is shown that a unique dispersion relation exists if the lighter fluid lies beneath the heavier one. However, if the heavier fluid lies beneath the lighter fluid, then no unique dispersion relation exists. The effect of rotation is to slow down the rate at which potentially unstable stratification departs from the equilibrium position.     

Effect of quantum corrections on the Jeans instability of self-gravitating viscoelastic dusty fluid

In this paper we investigate the effects of quantum correction on the Jeans instability of self-gravitating viscoelastic dusty electron-ion quantum fluids. The massive self-gravitating dust grains are assumed to be strongly coupled and non-degenerate having both viscous and elastic behavior while the inertialess electrons and ions are considered as weakly coupled and Fermi degenerate. The hydrodynamic model is modified and a linear dispersion relation is derived employing the plane wave solutions on the linearized perturbation equations for the considered system. It is observed that the dispersion properties are affected due to the presence of viscoelastic effects and quantum statistical corrections. The modified condition of Jeans instability and expression of critical Jeans wavenumber are obtained. Numerically it is shown that viscoelastic effects, dust plasma frequency and quantum statistical effects all have stabilizing influence on the growth rate of gravitationally Jeans mode. The growth rates are also compared in kinetic and hydrodynamic limits and it is found that decay in the growth of unstable Jeans mode is larger under the kinetic limits than the hydrodynamic limits. The results are discussed for the understanding of formation of dense degenerate dwarf star through gravitational collapsing which is assumed to be strongly coupled dusty quantum fluid where the strongly coupled dust provides inertia and Fermi degenerate electron and ions provide quantum statistical effects.     

Magneto-gravitational instability of a fluid through porous medium including finite ion Larmor radius

The magneto-gravitational instability of an infinite, homogenous, and infinitely conducting plasma flowing through a porous medium is studied. The finite ion Larmor radius (FLR) effects and viscosity are also incorporated in the analysis. The prevalent magnetic field is assumed to be uniform and acting in the vertical direction. A general dispersion relation has been obtained from the relevant linearized perturbation equations of the problem. The wave propagation parallel and perpendicular to the direction of the magnetic field have been discussed. It is found that the condition of the instability is determined by the Jeans criterion for a self-gravitating, infinitely conducting, magnetized fluid through a porous medium. Furthermore, for transverse perturbation FLR is found to have stabilizing influence when the medium is considered inviscid.     

Magnetogravitational stability of self-gravitating plasma with thermal conduction and finite Larmor radius through porous medium

The problem of incipient fragmentation of interstellar matter to form condensation is investigated taking into account the porosity, viscosity, thermal conductivity, and effect of finite ion-Larmor radius (FLR) on the self-gravitating plasma having a uniform magnetic field acting in vertical direction. Relevant linearized equations are stated and dispersion relation is obtained. Wave propagation in longitudinal and transverse direction to the magnetic field is considered. Stability and instability of the medium is discussed. It is found that if the Jeans's instability condition is not fulfilled the medium must remain stable. Magnetic field, FLR and porosity do not affect the Jeans's criterion of instability in longitudinal direction but in transverse direction, the magnetic field and FLR have stabilizing effect which is reduced due to porosity of the medium. Thermal conductivity destabilizes the medium in both the directions. In transverse direction contribution of FLR on the Jeans's expression for instability is not observed in thermally conducting medium.     

Rayleigh–Taylor instability in an ionized medium

We study the linear theory of the magnetized Rayleigh–Taylor instability in a system consisting of ions and neutrals. Both components are affected by a uniform vertical gravitational field. We consider ions and neutrals as two separate fluid systems that can exchange momentum through collisions. However, ions have a direct interaction with the magnetic field lines but neutrals are not affected by the field directly. The equations of our two-fluid model are linearized and by applying a set of proper boundary conditions, a general dispersion relation is derived for our two superposed fluids separated by a horizontal boundary. We found two unstable modes for a range of wavenumbers. It seems that one of the unstable modes corresponds to the ions and the other one is for the neutrals. Both modes are reduced with increasing particle collision rate and ionization fraction. We show that if the two-fluid nature is considered, the RT instability would not be suppressed and we also show that the growth time of the perturbations increases. As an example, we apply our analysis to the Local Clouds which seem to have arisen because of the RT instability. Assuming that the clouds are partially ionized, we find that the growth rate of these clouds increases in comparison to the fully ionized case.     

Gravitational instability of a heat-conducting plasma

The gravitational instability of an infinite, anisotropic, heat-conducting plasma is studied in this paper. It is found that, for the case of parallel propagation, the inclusion of heat-conduction terms in the fluid equations, in general, leads to overstability of the system, whereas the transverse propagation remains unaffected. We have solved numerically the dispersion relation corresponding to the parallel propagation and find that except for a range of wave numbers, the system is overstable. We also found that in the limit of vanishing zeroth-order heat flux, the condition for gravitational instability is similar to the Jeans's condition for instability for an isotropic plasma.     

Effect of nonthermality on the perturbation dynamics of self-gravitating complex fluids

The perturbation dynamics of an unbounded nonthermal self-gravitating inhomogeneous viscoelastic system composed of two-component constitutive fluids is theoretically investigated. The role of fluid turbulence, which is a highly nonlinear hydrodynamic vorticity-driven phenomenology, is included via the Larson logatropic equation of state describing nonlinear fluid pressure effects. The thermodynamics of the variable-temperature bulk fluid is included with the help of a proper heat diffusion equation. The system is coupled by the electro-gravitational Poisson equations in a closed form. A generalized linear dispersion relation (cubic in degree) is procedurally obtained using a standard technique of linear normal mode analysis. The dispersion relation stems from the rudimentary condition of non-vanishing perturbed gravitational potential in a linear order. The propagatory and dispersive features of the composite fluid perturbations are numerically explored with a special attention to the nonthermality effects. Their growth characteristics are analyzed alongside promising indication to applicability in the astro-cosmo-plasmic context.     

Gravitational instability of a thermally-conducting plasma flowing through a porous medium in the presence of suspended particles

Magnetogravitational instability of a thermally-conducting, rotating plasma flowing through a porous medium with finite conductivity and finite Larmor radius in the presence of suspended particles has been investigated. The wave propagation has been considered for both parallel and perpendicular axes of rotation. Magnetic field is being taken in the vertical direction. A general dispersion relation has been derived through relevant linearized perturbation equations. It has been observed that the condition of instability is determined by the Jeans's criterion in its modifed form. Thermal conductivity replaces the adiabatic velocity of sound by the isothermal one. Rotation decreases the Larmor radius. Porosity decreases the Alfvén velocity. In case of a viscous medium the effects of FLR, rotation, and suspended particles are not observed in the Jeans's condition, for transverse propagation for rotational axis parallel to the magnetic field. The effects of rotation and FLR are decreased by the porosity and the suspended particles. Finite conductivity removes the Alfvén velocity from Jeans's condition.     

Gravitational instability of a rotating partially-ionized plasma carrying a uniform magnetic field with hall effect

The problem of gravitational instability of an infinite homogeneous self-gravitating medium carrying a uniform magnetic field in the presence of Hall effect has been investigated to include the effect due to rotation. The dispersion relation has been obtained. It has been found that the Jeans's criterion for the instability remains unaffected even when the effect due to rotation is considered in the presence of Hall effect carrying a uniform magnetic.     

Nonlinear waves in superposed fluids

A weakly nonlinear theory of wave propagation in superposed fluids in the presence of magnetic fields is presented in this paper. We derive the equations governing the evolution of the amplitude of the progressive as well as the standing waves. It is demonstrated that the waves can be unstable against modulation in the presence of the magnetic fields. We also obtain the nonlinear cut off wave number which separates the region of stability from instability.     

Magnetogravitational instability of an infinite homogeneous rotating plasma through a porous medium with finite electrical and thermal conductivities

The gravitational instability of an infinite homogenous rotating plasma through a porous medium in the presence of a uniform magnetic field with finite electrical and thermal conductivities has been studied. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained, which is further reduced for the special cases of rotation, parallel and perpendicular to the megnetic field acting in the vertical direction. Longitudinal and transverse modes of propagation are discussed separately. It is found that the joint effect of various parameters is simply to modify the Jeans's condition of instability. The effect of finite electrical conductivity is to remove the effect of magnetic field where as the effect of thermal conductivity is to replace the adiabatic velocity of sound by the isothermal one. Rotation has its effect only along the magnetic field in the transverse mode of propagation for an inviscid plasma, thereby stabilizing the system. Porosity reduces the effect of both, the magnetic field and the rotation, in the transverse mode of propagation in both the cases of rotation. The effect of viscosity is to remove the rotational effects parallel to the magnetic field in the transverse mode of propagation.     

Nonlinear Kelvin-Helmholtz instability in hydromagnetics

By taking into account the temporal as well as the spatial effects, a weakly nonlinear theory of the propagation of wave packets in the Kelvin-Helmholtz instability problem in the presence of uniform magnetic fields, acting along the surface of separation of two moving superposed fluids, is presented. With the use of the method of multiple scaling, the evolution of the amplitude of the two-dimensional wave packets, which is governed by a nonlinear Klein-Gordon equation, is derived. The various stability criteria arising out of this equation are examined. The nonlinear cut-off wavenumber, which separates the region of stability from that of instability, is determined.     

Self-gravitational instability of rotating viscous Hall plasma with arbitrary radiative heat-loss functions and electron inertia

The effects of arbitrary radiative heat-loss functions and Hall current on the self-gravitational instability of a homogeneous, viscous, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, finite electron inertia and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis with the help of relevant linearized perturbation equations of the problem, and a modified Jeans criterion of instability is obtained. The conditions of modified Jeans instabilities and stabilities are discussed in the different cases of our interest. We find that the presence of arbitrary radiative heat-loss functions and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. For longitudinal propagation, it is found that the condition of radiative instability is independent of the magnetic field, Hall parameter, finite electron inertia, finite electrical resistivity, viscosity and rotation; but for the transverse mode of propagation it depends on the finite electrical resistivity, the strength of the magnetic field, and it is independent of rotation, electron inertia and viscosity. From the curves we find that the presence of thermal conductivity, finite electrical resistivity and density-dependent heat-loss function has a destabilizing influence, while viscosity and magnetic field have a stabilizing effect on the growth rate of an instability. The effect of arbitrary heat-loss functions is also studied on the growth rate of a radiative instability.