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1.
Ian W. Roxburgh 《Astrophysics and Space Science》1974,27(2):425-435
The structure of self-gravitating, inviscid, compressible fluids is investigated assuming a polytropic relation between pressure and density. A class of solutions with non-uniform rotation and internal meridian circulation are presented and the stream lines of the flow calculated using a perturbation technique. 相似文献
2.
The shape of the Earth and of planets depends on the exciting forces and on the rheology of the medium. From the equilibrium equation, we present the main modelisations of the viscous and inviscid fluids and we essentially describe the characteristics of linear viscoelastic deformations, for the Maxwell viscoelastic model of rheology. We use the elastic, viscoelastic and fluid Love numbers in order to investigate the associated relaxation modes. For these various kinds of rheology of the planets interior, we compute the geoid and the topography induced by an internal mass distribution. Finally, we show the importance of this viscoelastic deformation calculations in the study of the celestial body rotations. 相似文献
3.
The instability of nonhomentropic axisymmetric flows of ideal fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. This problem is important in studying the dynamics of astrophysical flows as shear fluid flows around a gravitating center. A complex influence of a nonzero entropy gradient on the instability of sonic and surface gravity modes has been found. In particular, both an increase and a decrease in entropy against the effective gravity g eff causes the growth of surface gravity modes that are stable at the same parameters for a homentropic flow. At the same time, the growth rate of the sonic instability branches either monotonically increases with increasing rate of decrease in entropy against g eff or becomes zero at both negative and positive entropy gradients in the unperturbed flow. Calculations also show that growing internal gravity modes appear in the problem with free boundaries under consideration only if the flow is no longer stable with respect to axisymmetric perturbations. In addition, we show that it is improper to specify the entropy distribution in the main flow by a polytropic law with a polytropic index different from the adiabatic value, since the perturbation field does not satisfy the boundary condition at a free boundary in this case. 相似文献
4.
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. 相似文献
5.
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. 相似文献
6.
The linear self-gravitational instability of finitely conducting, magnetized viscoelastic fluid is investigated using the modified generalized hydrodynamic (GH) model. A general dispersion relation is obtained with the help of linearized perturbation equations using the normal mode analysis and it is discussed for longitudinal and transverse modes of propagation. In longitudinal propagation, we find that Alfven mode is uncoupled with the gravitating mode. The Jeans criterion of instability is determined which depends upon shear viscosity and bulk viscosity while it is independent of magnetic field. The viscoelastic effects modify the fundamental Jeans criterion of gravitational instability. In transverse mode of propagation, the Alfven mode couples with the acoustic mode, compressional viscoelastic mode and gravitating mode. The growth rate of Jeans instability is compared in weakly coupled plasma (WCP) and strongly coupled plasma (SCP) which is larger for SCP in both the modes of propagations. The presence of finite electrical resistivity removes the effect of magnetic field in the condition of Jeans instability and expression of critical Jeans wavenumber. It is found that Mach number and shear viscosity has stabilizing while finite electrical resistivity has destabilizing influence on the growth rate of Jeans instability. 相似文献
7.
The magnetoacoustic modes excited in a thermally conducting polytropic fluid layer in the presence of a vertical magnetic field are examined with a view to classify them with the help of phase diagrams. The possibility of identifying the umbral flashes with overstable magnetoacoustic modes is explored. 相似文献
8.
N.H. Bian 《Astronomische Nachrichten》2007,328(8):756-759
The resistive tearing instability of a sheet pinch, first investigated by Kuang & Roberts (1990) for the case of a rapidly rotating inviscid fluid, is studied for arbitrary rotation rate in a visco‐resistive fluid. Altogether there are three regimes of the resistive tearing instability which correspond to the particular parameter domain in the (Ω, Pm) plane. Here Ω is the angular velocity of the medium which is normalized to the Alfvén time and Pm is the magnetic Prandtl number. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
Ogilvie 《Monthly notices of the Royal Astronomical Society》1998,297(1):291-314
The theory of waves and instabilities in a differentially rotating disc containing a poloidal magnetic field is developed within the framework of ideal magnetohydrodynamics. A continuous spectrum, for which the eigenfunctions are localized on individual magnetic surfaces, is identified but is found not to contain any instabilities associated with differential rotation. The normal modes of a weakly magnetized thin disc are studied by extending the asymptotic methods used previously to describe the equilibria. Waves propagate radially in the disc according to a dispersion relation which is determined by solving an eigenvalue problem at each radius. The dispersion relation for a hydrodynamic disc is re-examined and the modes are classified according to their behaviour in the limit of large wavenumber. The addition of a magnetic field introduces new, potentially unstable, modes and also breaks up the dispersion diagram by causing avoided crossings. The stability boundary to the magnetorotational instability in the parameter space of polytropic equilibria is located by solving directly for marginally stable equilibria. For a given vertical magnetic field in the disc, bending of the field lines has a stabilizing effect and it is shown that stable equilibria exist which are capable of launching a predominantly centrifugally driven wind. 相似文献
10.
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. 相似文献
11.
Ahmed E. Radwan 《Astrophysics and Space Science》1992,191(2):307-312
The fundamental equations are formulated using cylindrical polar coordinates and then solved in the unperturbed state. The perturbation equations are determined, simplified, integrated and the constants of integrations are identified by applying appropriate boundary conditions across the perturbed fluid interface. A cumbersome stability criterion for MHD inviscid compressible self-gravitating streaming fluid cylinder is derived. The magnetic field is stabilizing, the streaming is destabilizing while both of the self-gravitating and compressibility are stabilizing or not according to restrictions and that the gravitational instability of sufficiently long waves will persist. Several approximations are required to obtain Chandrasekhar's and Fermi's dispersion relation (Chandrasekhar and Fermi, 1953). 相似文献
12.
Non-linear equations governing the temporal evolution of the vector of instantaneous rotation are developed for an Earth with a homogeneous mantle having a viscoelastic Maxwell rheology and with a homogeneous inviscid fluid core.This general theory is investigated using the angular momentum theorem applied to the coupled core-mantle system. It allows to study the influence upon the planetary rotation of a quasi-rigid rotational motion in the liquid core. It also enables to investigate the consequences of excitation sources (e.g. pressure), located at the core-mantle interface. Especially, the influence of viscoelastic variations in the inertia tensors resulting from the rotation itself or from various excitation sources are detailed with the help of a Love number formalism. The equations of the linear theory for an elastic Earth with a liquid core, and the non-linear theory for a viscous planet with a quasi-fluid behavior are shown to be particular cases of our generalized system of equations. Some planetological applications may be derived from the quasi-fluid approximation. 相似文献
13.
Kelvin-Helmholtz instability of the interface separating two viscous rotating-conducting fluids has been studied in the presence of finite ion-Larmor radius (FLR) effects. Emloying the normal mode technique, the solutions have been obtained when the fluids are assumed to be permeated by a uniform horizontal magnetic field. For the case of two highly viscous fluids, the dispersion relation has been derived and solved numerically. It is found that the streaming velocity has a stabilizing influence on the potentially unstable arrangement of the fluids. The viscosity and FLR effects are also found to have a stabilizing influence while the Coriolis forces have a destabilizing influence on the system. 相似文献
14.
There are several astrophysical situations where one needs to study the dynamics of magnetic flux in partially ionized turbulent plasmas. In a partially ionized plasma, the magnetic induction is subjected to the ambipolar diffusion and the Hall effect in addition to the usual resistive dissipation. In this paper, we initiate the study of the kinematic dynamo in a partially ionized turbulent plasma. The Hall effect arises from the treatment of the electrons and the ions as two separate fluids and the ambipolar diffusion due to the inclusion of neutrals as the third fluid. It is shown that these non-ideal effects modify the so-called α effect and the turbulent diffusion coefficient β in a rather substantial way. The Hall effect may enhance or quench the dynamo action altogether. The ambipolar diffusion brings in an α which depends on the mean magnetic field. The new correlations embodying the coupling of the charged fluids and the neutral fluid appear in a decisive manner. The turbulence is necessarily magnetohydrodynamic with new spatial and time-scales. The nature of the new correlations is demonstrated by taking the Alfvénic turbulence as an example. 相似文献
15.
A thin gaseous disk with a nearly Keplerian rotation profile and free boundaries in the external gravitational field of a
point gravitating object does not generate any growing perturbation eigenmodes. In spite of this, a significant transient
growth of linear perturbations measured by the evolution of their total acoustic energy is possible in such a disk. This is
shown within the framework of the simplest model of an inviscid polytropic thin disk with a finite radial extent in which
small adiabatic perturbations that are a linear combination of neutral eigenmodes with a corotation radius beyond the outer
flow boundary are considered. 相似文献
16.
J. A. WOOD 《Meteoritics & planetary science》1996,31(5):641-645
Abstract— A widely held view of nebular evolution is that during the ～0.5 Ma while interstellar material was collapsing onto the disk, the latter grew in mass to the point of gravitational instability. It responded to this by losing axial symmetry, growing spiral arms that had the capacity to tidally redistribute disk mass (inward) and angular momentum (outward) and prevent further increase in the disk/protosun mass ratio. The spiral arms (density waves) rotated differently than the substance of the nebula, and in some parts of the disk, nebular material may have encountered the arms at supersonic velocities. The disk gas, and solid particles entrained in it, would have been heated to some degree when they passed through shock fronts at the leading edges of the spiral arms. The present paper proposes this was the energetic nebular setting or environment that has long been sought, in which the material now in the planets and chondritic meteorites was thermally processed. 相似文献
17.
Zdeněk Kopal 《Astrophysics and Space Science》1968,1(3):284-300
The aim of the present paper will be to deduce the explicit form of differential equations which govern dynamical tides in close binary systems, with simplifications which are permissible for the mass-point model (Section 2), as well as for one exhibiting finite but high internal density concentration (Section 3). It is pointed out that, whereas the exact formulation of the problem leads to a simultaneous system of equations of sixth order (fourth in the inviscid case), this order reduces to four (or two for inviscid fluids) for the mass-point model; and to five (three for inviscid case) if the density concentration is high but finite.In the last section of this paper the coefficientsC
i,j which specify the amplitudes of the individual partial tides are explicitly formulated as functions of the time. 相似文献
18.
The self-gravitating instability of an infinitely extending axisymmetric cylinder of viscoelastic medium permeated with non uniform magnetic field and rotation is studied for both the strongly coupled plasma (SCP) and weakly coupled plasma (WCP). The non uniform magnetic field and rotation are considered to act along the axial direction of the cylinder. The normal mode method of perturbations is applied to obtain the dispersion relation. The condition for the onset of gravitational instability has been derived from the dispersion relation under both strongly and weakly coupling limits. It is found that the Jeans criterion for gravitational collapse gets modified due to the presence of shear and bulk viscosities for the SCP, however, the magnetic field and rotation whether uniform or non uniform has no effect on the Jeans criterion of an infinitely extending axisymmetric cylinder of a self-gravitating viscoelastic medium. 相似文献
19.
《New Astronomy Reviews》1999,43(6-7):431-435
New results are presented from high resolution images of the peculiar T Tauri star V1331 Cyg and its nebular environment. A complex nebular fountain-like structure that appears to originate from the star was found. The morphology of the nebular structure is quantified and discussed. Evidence for secular outflows is found from the optical data. 相似文献
20.
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. 相似文献