The instability of a stratified layer of rotating and conducting self-gravitating fluid

Instability of a horizontal rotating layer of a self-gravitating electrically conducting fluid has been studied to simultaneously, include the effects of Hall currents and magnetic resistivity. The prevailing magnetic field is uniform and acts along the vertical direction along which the fluid has a one-dimensional density gradient. The solution has been obtained through the variational methods. The dispersion relation obtained has been solved numerically and it is found that Hall currents as well as magnetic resistivity have a destabilizing influence. Coriolis forces, however, have a stabilizing influence.     

Effects of Hall currents and Coriolis forces on the instability of a self-gravitating plasma of variable density

The hydromagnetic instability of a self-gravitating, incompressible rotating plasma of variable density has been examined in the presence of Hall currents. The system is assumed to be permeated by a variable horizontal magnetic field. The solution of the relevant linearized perturbation equations has been obtained by the normal mode technique through a variational principle which is shown to characterize the problem. Proper solutions have been obtained for a semi-infinite plasma having exponential density stratification along the vertical. The dispersion relation has been derived and solved numerically for different values of the physical parameters involved. It is found that Hall currents and Coriolis forces have both destabilizing influence as the growth rate of the unstable modes is found to increase with the increase of both Hall currents and Coriolis forces.     

Larmor radius effects on the instability of a rotating layer of a self-gravitating plasma

The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.     

Magnetic resistivity and Hall currents effects on the stability of a self-gravitating plasma of varying density in variable magnetic field

The effect of Hall currents have been studied on the instability of a stratified layer of a self-gravitating finitely conducting plasma of varying density. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. The stability analysis has been carried out for longitudinal mode of wave propagation. The solution has been obtained through integral equation approach. The dispersion relation has been derived and solved numerically. It is found that both the Hall currents and finite conductivity have a destabilizing influence on the growth rate of the unstable mode of disturbance.     

Dynamical stability of a self-gravitating rotating cylinder in a helical magnetic field

The effect of a helical magnetic field on the oscillations and the stability of a homogeneous self-gravitating rotating cylinder is investigated. The axial field has a tendency to stabilise long wave numbers and to destabilise small wave numbers so that maximum instability occurs for a finite wave number. If the toroidal and the axial component of the field have the same sign, the instability associated with the toroidal field can be removed by the rotation or by the axial field. Rotational instability is reduced but cannot removed by the field. If the components of the field have the opposite sign, rotational instability is increased. The maximum growth rate of the magnetic instability is reduced by a small axial field and tends to a finite value for large axial fields.     

Wall temperature oscillation on convection flow in a rotating fluid with hall and ion-slip currents

An analysis of Hall and ion-slip current effects on the MHD free-convection flow of a partiallyionised gas past an infinite vertical porous plate in a rotating frame of reference is carried out. A strong magnetic field is applied perpendicular to the plate and the plate temperature oscillates in time about a constant non-zero mean. The problem has been solved for the velocity and temperature fields and the effects of _e (the Hall parameter), _i (the ion-slip parameter),E _r (rotation parameter), and have been discussed and shown graphically.     

Finite larmor radius and hall effects on thermosolutal instability of a rotating plasma

Thermosolutal instability of a rotating plasma with finite Larmor radius and Hall effects is studied. When the instability sets in as stationary convection, the Hall currents and the stable solute gradient are found to have destabilizing and stabilizing effects, respectively. For the case of no rotation, finite Larmor radius effects are always stabilizing forx greater than two and forx less than its critical valueN _cr. In the limit of vanishing Hall current, the stabilizing effect of Coriolis force is observed. The question of onset of instability as overstability is also discussed.     

Finite Larmor radius effects on the stability of a stratified plasma

The hydromagnetic stability of a cosmical plasma interacting with neutral gas has been studied to include the effects of ion viscosity and the finiteness of the ion Larmor radius. It is first shown that the system is characterized by a variational principle. The explicit solution has then been obtained, by making use of the existence of the variational principle, for a semi-infinite plasma in which the density is stratified, exponentially, along the vertical. It is found that FLR, ion viscosity as well as neutral gas friction have all a stabilizing influence.     

Linear stability of a self-gravitating ring

Stability of a self-gravitating ring about a central body is considered. The purpose is to derive a bound on the mass of the ring in order that the system will be linearly stable. Our bound will, in some cases, be the best possible bound. The bound is also expanded as an asymptotic series. Comparisons of our result are made with respect to previous analyses performed by Tisserand, Pendse and Willerding.     

Dynamical and secular instability of a homogenous self-gravitating rotating cylinder

The non-axisymmetric oscillations and stability of a homogeneous self-gravitating rotating cylinder are investigated. Two infinite discrete spectra of rotational modes arises. Dynamical and secular instability occur for wavelengths situated in a certain interval, if ²>(m – 1 )/2m where denotes the angular velocity andm the azimuthal wave-number. Modes of maximum instability and maximum growth rates are determined. Viscosity reduces the growth rate of smaller wavelengths but increases the instability of the longer wavelengths. We show that the onset of secular instability is associated with a point of neutral oscillation.     

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.     

Effects of hall current on the hydromagnetic free convection with mass transfer in a rotating fluid

An exact analysis of Hall current on hydromagnetic free convection with mass transfer in a conducting liquid past an infinite vertical porous plate in a rotating fluid has been presented. Exact solution for the velocity field has been obtained and the effects ofm (Hall parameter),E (Ekman number), andS _c (Schmidt number) on the velocity field have been discussed.Nomenclature C species concentration - C _w concentration at the porous plate - C species concentration at infinity - C _p specific heat at constant pressure - D chemical molecular diffusivity - g acceleration due to gravity - E Ekman number - G Grashof number - H ₀ applied magnetic field - j _x, j_y, j_z components of the current densityJ - k thermal conductivity - M Hartman number - m Hall parameter - P Prandtl number - Q heat flux per unit area - S _c Sehmidt number - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid in the free-stream - u, v, w components of the velocity fieldq, - U uniform free stream velocity - w ₀ suction velocity - x, y, z Cartesian coordinates - Z dimensionless coordinate normal to the plate. Greek symbols coefficient of volume expansion - ^* coefficient of expansion with concentration - _e cyclotron frequency - dimensionless temperature - ^* dimensionless concentration - v kinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - _e magnetic permeability - angular velocity - electrical conductivity of the fluid - _e electron collision time - _u skin-friction in the direction ofu - _v skin-friction in the direction ofv     

Larmor radius effects on the instability of a stratified partially-ionized plasma in the presence of Hall currents and magnetic resistivity

Instability of a stratified layer of a partially-ionized plasma has been investigated in the simultaneous presence of the effects of Hall currents, magnetic resistivity, finite Larmor radius (FLR), and viscosity. The ambient magnetic field is assumed to be uniform and acting along the vertical direction. The solution is shown to be characterized by a variational principle, based on it the solution has been obtained for a plasma in which the density is stratified exponentially along the vertical. It is found that the viscosity, friction with neutrals, and FLR have all stabilizing influence on the growth rate of the unstable mode of disturbance. Magnetic resistivity and Hall currents are, however, found to have a destabilizing influence.     

The stability of a magnetic flux element in a horizontally stratified compressible plasma

The configuration of a magnetic flux element in a static, compressible, gravitationally stratified plasma is considered. Under isothermal conditions an exact force-free solution is given for a two-dimensional cartesian flux sheath but for an axi-symmetric element, i.e. a flux tube, approximate solutions, applicable only to thin flux tubes, are obtained.When the isothermal condition is relaxed within the flux tube, non-force-free solutions are obtained exhibiting either a temperature excess or deficit on the axis of the flux tube. Using these solutions, the total potential energy of such a tube and its surroundings may be calculated. By comparing this with the total energy of an equivalent system ofn flux tubes the temperature excess or deficit in these tubes corresponding to the adiabatic subdivision of the single tube is determined.It is shown that under non-adiabatic conditions the subdivision process must be endothermic (i.e., external energy is required) if the temperature within the original tube is significantly less than its surroundings but exothermic if the temperatures are comparable. Thus it is conjectured that magnetic structures are less susceptible to subdivision if they are significantly cooler than their surroundings.     

Dynamical and secular instability of a self-gravitating rotating cylinder in a toroidal magnetic field

The oscillations and stability of a homogeneous self-gravitating rotating cylinder in a toroidal magnetic field are investigated. It is assumed that the field is proportional to the distance to the axis of the cylinder. We show the existence of four infinite discreta spectra of magnetic (or rotational) modes. Rotation stabilizes the magneticm=1 instability. The magnetic field decreases the growth rate of rotational instability and reduces the interval of unstable wavenumbers. Ifm=1, instability always occurs with the exception of the equipartition state. Ifm>1, the instability can be suppressed by a sufficiently large magnetic field. Resistivity decreases the growth rate of magnetic instability, but increases the growth rate of rotational instability. For zero wavenumber perturbations secular instability occurs due to the action of resistivity before a neutral point is attained where a second secular instabiliity initiates due to the action of resistivity.     

A note on the stability of one-dimensional self-gravitating isothermal systems

One-dimensional self-gravitating isothermal systems are stable with respect to one-dimensional perturbations.     

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.     

On the stability of strongly non-homogeneous self-gravitating equilibria

The stability analysis of several stronglynon-homogeneous, self-gravitating, one-dimensionalunstable equilibrium systems is carried out with the help of numerical techniques. The evolution of the perturbed unstable equilibria is studied by following the motion of the boundary curves of water bag configurations defining the systems.It is found that initial perturbations drive the unstable equilibrium states out of equilibrium at rates depending on the typical scale length of the perturbations : the instability rates increase with .     

Strong spherical shock wave propagation in a self-gravitating RMHD rotating interplanetary medium

In the present paper, we have discussed the propagation of spherical shock waves in a radiating magnetohydrodynamic rotating interplanetary medium. The effects of force of self-gravitation have been taken into account with the assumption that at the equilibrium position the effects of rotation on the force of gravitation are negligible. The combined effects of rotation and gravitation on the variation of flow variables have been shown in tables. The particular cases of the problem have been discussed and compared by considering effects of rotation and gravitation separately.