Hydromagnetic gravitational instability of an infinite cylinder of a compressible fluid

The gravitational instability of an infinite cylinder of a self-gravitating, perfectly-conducting, compressible fluid subjected to a uniform axial magnetic field is investigated. A generalised dispersion relation describing the stability characteristics of the configuration is given. The gravitational instability of the cylinder is found to be worsened in the presence of the compressibility effects in the fluid.     

Nonaxisymmetric magnetogravitational instability of a streaming fluid cylinder ambient with a tenuous medium pervaded by transverse varying fields

The stability of a self-gravitating streaming fluid cylinder acting upon the electromagnetic force ambient with a tenuous medium of negligible inertia but pervaded by a transverse varying fields, has been developed. The stability criterion is derived, discussed analytically and the results are verified numerically. The cylinder is purely self-gravitating unstable in small axisymmetric domain and stable in all the rest states. modes while the transverse field exterior the cylinder is stabilizing or destabilizing according to restrictions in the asymmetric modes and purely destabilizing in the symmetric one. The streaming has a strong destabilizing influence and that influence is independent of the kind of the perturbation and wavelengths. Both the streaming and the electromagnetic influences increase the gravitational axisymmetric unstable domain and shrink those of stability in the axisymmetric and non-axisymmetric perturbations. Moreover, the stabilizing character of the Lorentz force of some states, is physicaly interpreted, will not be able to suppress the gravitational instability because the gravitational instability of sufficiently long waves will persist.     

Dynamical instability of laminar axisymmetric flows of ideal compressible fluid

The instability of axisymmetric flows of inviscid compressible fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The compressibility is taken into account for a homentropic flow with an adiabatic index varying over a wide range. The problem has been solved for two angular velocity profiles of an initial axisymmetric flow. In the first case, a power-law rotation profile with a finite enthalpy gradient at the flow edges has been specified. For this angular velocity profile, we show that the instability of sonic and surface gravity modes in a nearly Keplerian flow, when a radially variable vorticity exists in the main flow, can be explained by the combined action of the Landau mechanism and mode coupling. We also show that including a radially variable vorticity makes the limiting exponent in the rotation law at which the unstable surface gravity modes vanish dependent on the fluid compressibility. In the second case, a Keplerian rotation law with a quasi-sinusoidal deviation has been specified in such a way that the enthalpy gradient vanished at the flow edges. We have found than the sonic modes are then stabilized and the flow is unstable only with respect to the perturbations that also exist in an incompressible fluid.     

A heerarchical model for gravitational compressible tubrulence

We formulate a two-stage scheme for astrophysical turbulence in the frame of a revised Kolmogorov self-similar theory, hierarchical in nature. According to this approach, graviaation is revealed to be the main source of dissipated energy supporting the turbulent cascade. Results are compared with observational data about molecular clouds in the Galaxy and with the forecastings of an intermittent model of the same authors.     

The stability of stratified shear flows of an inviscid compressible fluid in MHD

By the generalized progressing wave expansion method, the effect of a magnetic field on the linear stability of the stratified horizontal flow of an inviscid compressible fluid has been studied. It is found that the magnetic field stabilizes the system.     

The jeans instability criterion for a compressible fluid including viscosity and heat conduction

For the region after the recombination era of the Universe the hydrodynamical density waves are analyzed including shear viscosity and heat conduction for =_c as well as for <_c(_c is the critical density of the Universe). Very near to the end of the recombination era (z=1200) we find the well-known Jeans instability. It is shown that the influence of the shear viscosity on the instabilities in negligible, however, a visible influence of the bulk viscosity is present.     

A note on the gravitational field of Phobos

Phobos' proximity to the Roche limit, and some of its consequences deserving attention by the Phobos' mission, are the subject of this note.     

Convective instability in a compressible atmosphere

The degree of convective instability as expressed by the growth rate of linear modes, is calculated for a plane parallel polytropic atmosphere in the presence of radiative damping, without using Boussinesq approximation. A comparison with the results based on the Boussinesq approximation reveals that the use of the Boussinesq approximation leads to an overestimation of the radiative damping. The computation of as a function of the horizontal wave number yields a wavelength of maximal instability under a variety of conditions. For reasonable choices of physical parameters appropriate to the solar atmosphere, the fastest growing wavelengths turn out to be in the range 600–1200 km, and their e-folding times are in the range 200–2000 s.NAS-NRC Senior Research Associate on leave of absence from the Tate Institute of Fundamental Research, Bombay.     

Stability of a compressible fluid cylinder ambient with a bounded conducting medium under general varying magnetic fields

The stability of a compressible fluid cylinder pervaded by a longitudinal uniform magnetic field-ambient with a bounded conducting medium of negligible inertia penetrated with general varying vacuum magnetic fields has been developed. The stability criterion describing the stability characteristics of that model is derived and discussed analytically in general terms. The axial fields have always stabilizing influences. The azimuthal vacuum field has a destabilizing effect, however, it becomes minimal if the perturbed and the unperturbed vacuum fields are not orthogonal. The magnetodynamic instability of the fluid jet is modified in the presence of the fluid compressibility. The stabilizing influence due to the latter may be realized more clearly on utilizing the numerical methods for investigating the eigenvalue relation.Several reported works can be recovered as limiting cases with appropriate simplifications.     

Theoretical density distribution of plasma streaming around a cylinder

The distribution of plasma density around a metallic cylinder in a collisionfree plasma is determined by the system of Vlassov equations and the Poisson equation. The plasma may have a streaming velocity perpendicular to the cylinder axis producing a wake behind the cylinder. In the region outside a thin double layer at the cylinder surface the problem allows some simplification. Then numerical solutions become possible-even if the streaming velocity is low. Some numerical solutions are presented. A magnetic field produces an asymmetric shape of the wake, if the gyration radius of the ion becomes comparable to the cylinder radius.     

A note on gravitational baryogenesis within Bianchi type I universe

The mechanism of gravitational baryogenesis, based on the CPT-violating gravitational interaction between the derivative of the Ricci scalar curvature. We study the gravitational baryogenesis in the Bianchi type I universe. We find out the effect of anisotropy of the universe on the baryon asymmetry for the different models of cosmology.     

Local potential analysis of MHD instability

In many astrophysical problems, the study of the stability of an atmosphere in the presence of a magnetic field is of importance. In most cases the MHD instabilities of atmospheres are studied by energy principle of Bernsteinet al. (1958). In this paper, a general method for studying the stability of a system subject to MHD equations of conditions has been proposed. This is based on the local potential concept put forward by Glansdorff and Prigogine (1964). The scheme for securing stability criteria has been demonstrated in two particular cases.     

Dissipation of MHD waves in an inhomogeneous streaming plasma

The investigation of instabilities adopting the point of view of inhomogeneous mass flow, physically corresponds to consideration of stability of the perturbations whose wavelengths in the direction of plasma inhomogeneities are much larger than the characteristic plasma scale length. The dissipation of hydromagnetic-waves and instabilities takes place due to the inhomogeneous plasma flow. Both the velocity and plasma density vary in the direction perpendicular to the magnetic field. It is found that the Alfvén wave branch and magnetosonic branch may be driven unstable by the velocity shear. Instability, oscillatory modes, marginal instability and overstability are worked out.     

A note on the mass-loaded MHD flow of the solar wind towards a cometary nucleus

Dependence of the central velocity gradients on Hubble's type is presented for 78 spiral galaxies with existing rotation curves. Also the dependence of the maximum rotational velocities of 27 galaxies on both Hubble's type and the luminosity is studied. The central velocity gradient is shown to be related with Hubble's type. Maximum rotational velocities of 27 galaxies of our sample depend on Hubble's type such that the mean values of maximum rotational velocity decrease from Sa through Sc. It is also determined that there is a dependence of the maximum rotational velocity on the absolute blue magnitude for each intrinsic Hubble type. For each Hubble type, maximum rotational velocity increases with increasing absolute blue magnitudes.     

On the influence of degeneracy on gravitational instability

The influence of degeneracy on gravitational instability in a collisionless particle system with a semi-degenerate distribution function is discussed. The collapse time and the Landau damping time are calculated. The influence of degeneracy on Jeans wave number and on stability have important implications in the theory of galaxy formation in a universe dominated by fermionic dark matter.     

Compressible,conductive, steady MHD flow in a gravitational field

The magnetohydrodynamics of a compressible fluid with finite electrical conductivity in a gravitational field is treated analytically. For the case of one ignorable coordinate in cylindrical and Cartesian coordinates the problem is reduced to a scalar partial differential equation. The ideal gas equation of state is considered. For simplicity, the new equation is derived for a two-component motion. The application of this result to mass flow in sunspots is discussed.     

Magnetogravitational instability of a finitely-conducting medium with variable streaming motion

A discussion of gravitational instability of a finitely conducting medium with streams of variable velocity distribution is made in the presence of a uniform magnetic field. It is found that the variable streaming motion shows a destabilizing effect and affects the instability criterion only in the case of general wave propagation. For purely parallel propagation to the direction of the magnetic field and the streaming motion, the criterion is independent of the variation in the streaming motion and further the Jeans's criterion is found to remain unaffected in this case. For purely transverse propagation, the criterion is independent of any streaming motion and the Jeans's criterion remains unaffected. The criterion is further independent of the magnetic field and the finite conductivity except in the case of transverse propagation where the magnetic field exhibits a stabilizing influence in case of an infinitely conducting medium.     

Finite Larmor radius effect on thermal instability of a compressible rotating plasma

Thermal instability of a compressible rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of finiteness of the ion-Larmor radius. When the instability sets in as stationary convection, the compressibility is found to have stabilizing effect. It is found that finite Larmor radius effects are always stabilizing forx greater than two and forx less than two they have a destabilizing influence in the presence of rotation. The stabilizing effect of coriolis force is observed and for the case of no rotation, finite Larmor radius effects are always stabilizing. The sufficient conditions for the nonexistence of overstability are investigated.     

Rayleigh-Taylor instability of a viscous compressible plasma of variable density

A study has been made of the problem of the Rayleigh-Taylor instability of a hydromagnetic plasma of varying density to investigate the influence of the simultaneous presence of the effects of compressibility and viscosity. The solution is shown to be characterized by a variational principle. Based on the variational principle proper solutions have been obtained for a semi-infinite plasma, in which the density has a one-dimensional gradient along the direction of a uniform vertical magnetic field, confined between two planes. Both the viscosity and magnetic field are found to have a stabilizing influence. The effect of compressibility is found to be destabilizing.     

Rayleigh instability of compressible plasma in a vertical magnetic field

A study of the Rayleigh instability of a compressible plasma of density stratified in horizontal planes and subjected to a vertical magnetic field is made. The special case of a plane interface separating two superposed uniform plasmas of different densities and speeds of sound is treated as an example to illustrate the compressibility effects on the hydromagnetic Rayleigh instability. It is found that the hydromagneticcompressibility effects act toward reducing the growth rate in a hydrodynamically unstable situation.