Anisotropic propagation of magnetogasdynamic sonic waves in conducting and radiating atmosphere

The propagation of sonic discontinuity in conducting and radiating atmosphere has been discussed under the influence of magnetic field. The velocity of sonic wave and its termination into shock wave has been obtained. We have also obtained the critical time at which sonic wave terminates into shock wave. There is significant effect of magnetic field on sonic velocity and its termination into shock wave.     

Non-uniform propagation of weak waves through thermally-conducting and dissociating gases

Non-uniform propagation of weak discontinuities headed by wavefronts of arbitrary shape along bi-characteristics of a hyperbolic system through thermally-conducting and dissociating gases are studied. An explicit criterion for the growth and decay of weak waves along bi-characteristic curves in the characteristic manifold of the governing differential equations is given. The two fundamental theorems on the global behaviour of the time-dependent wave amplitude of a weak wave has been concluded.     

Propagation of sonic waves in an optically thick medium in the presence of magnetic field

This paper studies sonic waves in an optically thick medium under the influence of a magnetic field. The conductivity of the medium has been taken to be infinite. The effects of radiation, radiation energy density, radiative heat transfer and magnetic field have been taken into account. It has been obtained that the magnetic field has significant effect on sonic velocity. The fundamental differential equations governing the growth and decay of sonic waves are determined and solved.     

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.     

Weak MHD discontinuities in a radiation-induced flow field

The growth of weak MHD discontinuities have been studied in a radiation induced flow field at very high temperature. Growth and decay properties of weak MHD discontinuities have been discussed under the influences of time-dependent gasdynamic field, the radiation field and the magnetic field with finite electrical conductivity. The effects of thermal radiation and conduction of the global behaviour of weak MHD discontinuities have been studied under a quasi-equilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative heat transfer equation. It is shown that the existence of the time-dependent radiation field gives rise to a radiation induced wave which has a negligibly small effect on the non-relativistic flow properties of the gasdynamic field. It is also shown that the radiation stresses resist the steepening tendency of a compressive weak wave and help in stabilizing it whereas the thermal conduction effects counteracts to destabilize it. It is found that under radiation effects the shock formation is either disallowed or delayed. The two cases of diverging waves and converging waves have been studied separately to answer a particular question as to when a shock discontinuity or a coustic will be formed or disallowed under curvature effects.     

Growth and decay of sonic waves in thermally radiative magnetogasdynamics

The propagation of weak discontinuities headed by a wavefront and their formation into shock waves are investigated in a thermally-radiative ideal plasma. It is found that all compressive waves grow without bound only if the magnitude of initial discontinuity associated with the wave exceeds a critical value. In particular, the grow and decay of weak discontinuities in plane, cylindrical, and spherical geometries have been discussed and the shock formation distance and time in all these cases have been derived in presence of magnetic field and radiation, separately.     

Dynamical instability of laminar axisymmetric flows of ideal fluid with stratification

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.     

Model dependence of the multi-transonic behaviour,stability properties and the corresponding acoustic geometry for accretion onto rotating black holes

Stationary, multi-transonic, integral solutions of hydrodynamic axisymmetric accretion onto a rotating black hole have been compared for different geometrical configurations of the associated accretion disc structures described using the polytropic as well as the isothermal equations of state. Such analysis is performed for accretion under the influence of generalised post Newtonian pseudo Kerr black hole potential. The variations of the stationary shock characteristics with black hole spin have been studied in details for all the disc models and are compared for the flow characterised by the two aforementioned equations of state. Using a novel linear perturbation technique it has been demonstrated that the aforementioned stationary solutions are stable, at least upto an astrophysically relevant time scale. It has been demonstrated that the emergence of the horizon related gravity like phenomena (the analogue gravity effects) is a natural consequence of such stability analysis, and the corresponding acoustic geometry embedded within the transonic accretion can be constructed for the propagation of the linear acoustic perturbation of the mass accretion rate. The analytical expression for the associated sonic surface gravity κ has been obtained self consistently. The variations of κ with the black hole spin parameter for all different geometric configurations of matter and for various thermodynamic equations of state have been demonstrated.     

Effective sound speed in relativistic accretion discs around Schwarzschild black holes

For low angular momentum axially symmetric accretion flow maintained in hydrostatic equilibrium along the vertical direction, the value of the Mach number at the critical points deviates from unity, resulting in the non-isomorphism of the critical and the sonic points. This introduces several undesirable complexities while analytically dealing with the stationary integral accretion solutions and the corresponding phase portraits. We propose that the introduction of an effective dynamical sound speed may resolve the issue in an elegant way. We linear perturb the full spacetime-dependent general relativistic Euler and the continuity equations governing the structure and the dynamics of accretion disc in vertical equilibrium around Schwarzschild black holes and identify the sonic metric embedded within the stationary background flow. Such metric describes the propagation of the linear acoustic perturbation inside the accretion flow. We construct the wave equation corresponding to that acoustic perturbation and find the speed of propagation of such perturbation. We finally show that the ordinary thermodynamic sound speed should be substituted by the speed of propagation of the linear acoustic wave which has been obtained through the dynamical perturbation. Such substitution will make the value of Mach number at the critical point to be equal to unity. Use of the aforementioned effective sound speed will lead to a modified stationary disc structure where the critical and the sonic points will be identical.     

Thermally driven motions in a gravitational atmosphere

Numerical solutions of the non-linear equations of fluid dynamics for a compressible inviscid initially isothermal atmosphere are given using Lax' method for the integration of the equations when discontinuities occur in the flow. The motion of the atmosphere is studied following the heating of a thin layer in the atmosphere. It is found that for a sufficiently large heat input the atmosphere strongly expands towards the regions of lower densities. In most cases a shock wave is formed which precedes the expanding region. The possible occurrence of thermally generated motions in the solar chromosphere is discussed.On leave from the University of Wyoming at Laramie, Wyoming.     

Gravitational stability of finitely conducting two-component plasma through porous medium

The gravitational stability of magnetized self-gravitating two-component plasma of finite conductivity flowing through porous medium is studied. Effect of magnetic field, porosity, viscosity, finite conductivity, and neutral gas friction is considered on the stability of the system. Dispersion relations are derived from linearized equations using normal mode analysis. Longitudinal and transverse wave propagations are discussed. On the basis of Hurwitz criterion, the stability of the system is discussed. It is found that Jeans's criterion determines the stability of the system. Jeans's expression depends on the sonic speeds in both the components. For transverse wave propagation in perfectly conducting plasma. Jeans's expression is modified due to magnetic field and porosity but in case of finitely conducting plasma the Jeans's expression remains unaltered. Collisional frequency, viscosity, permeability of the porous medium have damping effect.     

Launching of accretion disc winds along dynamo-generated magnetic fields

The problem of magnetic field generation and advection in accretion discs is considered, in the context of wind launching and angular momentum extraction. A dipole-symmetry solution of the dynamo equations is found, with force-free boundary conditions appropriate for matching to a wind solution. Consideration of the curved field geometry and diffusive nature of the disc enables the position of the sonic point to be calculated and related to the field inclination at the disc surface. A critical inclination of 20° to the horizontal results, for which the sonic point lies in the disc surface and there is no potential barrier to wind launching. Hence the wind mass-loss rate will only become excessive, leading to disc disruption, for large field bending. The compressional effect of the horizontal magnetic field enhances the wind mass flux.     

Propagation of weak discontinuities in a vibrationally-excited gas flow

Propagation of weak discontinuities headed by wavefronts of arbitrary shape in three dimensions are studied in vibrationally relaxing gas flow. The transport equations representing the rate of change of discontinuities in the normal derivatives of the flow variables are obtained, and it is found that the nonlinearity in the governing equations does not contribute anything to the vibrationally relaxing gas. An explicit criterion for the growth and decay of weak discontinuities along bi-characteristic curves in the characteristic manifold of the governing differential equations is given. A special case of interest is also discussed.     

Nonlinear Evolution of a 3D Inertial Alfvén Wave and Its Implication in Particle Acceleration

A simulation based on a pseudo-spectral method has been performed in order to study particle acceleration. A model for the acceleration of charged particles by field localization is developed for the low-\(\upbeta\) plasma. For this purpose, a fractional diffusion approach has been employed. The nonlinear interaction between a 3D inertial Alfvén wave and a slow magnetosonic wave has been examined, and the dynamical equations of these two waves in the presence of ponderomotive nonlinearity have been solved numerically. The nonlinear evolution of the inertial Alfvén wave in the presence of slow magnetosonic wave undergoes a filamentation instability and results in field intensity localization. The results obtained show the localization and power spectrum of inertial Alfvén wave due to nonlinear coupling. The scaling obtained after the first break point of the magnetic power spectrum has been used to calculate the formation of the thermal tail of energetic particles in the solar corona.     

Kink mode <Emphasis Type="Italic">m</Emphasis> = 1 in a thin plasma filament with discontinuous vertical magnetic field

In this paper, we study the conditions of realization and stability of kink modes with azimuthal wave numbers m = ±1 in a cylindrical plasma filament with a twisted magnetic field and a homogeneous current along its axis. We assume that there are vertical constant magnetic fields inside and outside of the filament; the filament is surrounded by current-free plasma; and outside of its boundary, the azimuthal magnetic field decreases inversely in proportion to the distance from the filament’s border. The dispersion equations for stable and unstable modes are obtained in the approximation of “thin” plasma filament. The analysis of the equations for the case of discontinuous vertical magnetic field at the filament’s boundary is provided. The conditions of propagation of the wave modes have been defined. We have obtained that the unstable modes with m = ±1 cannot be realized. The results of this work can be applied to the interpretation of the solar magnetic flux tubes’ behavior using measurements provided by the spacecrafts.     

On the spectrum of some singular equations in magnetohydrodynamics

A class of singular differential equations that often occurs in problems in magnetohydrodynamics, plasma physics, and astrophysics is studied; first by means of the specific and fairly straightforward example of motions in a stratified magnetofluid, and secondly in terms of the nature of the eigenvalue spectrum for the more general class of problems. It is shown that in the absence of discontinuities in the basic profiles, the eigenvalue spectrum is real and continuous, and no discrete spectrum exists. Bounds are obtained on the location of the continuous spectrum.     

Wave systems in the chromosphere

Observations are reported of two, possibly three, distinct wave systems in the Hα chromosphere.

1. Velocity films show waves propagating predominantly outwards along mottles and fibrils from as close as 2000 km to the network axis at velocities of the order of 70 km s^-1. The line-of-sight component of the velocity amplitude is estimated to be typically 5 km s^-1. The velocities are accompanied by propagating intensity fluctuations. The system is interpreted as one of basically Alfvén waves. Similar waves are observed propagating predominantly outwards along superpenumbral fibrils radiating from a small sunspot.
2. The velocities in the chromospheric granulation undergo fluctuations of an oscillatory character but without any observable horizontal propagation. The intensities show a close correlation with the velocities, maximum intensity occurring about T/4 after maximum downward velocity. The period is variable across the surface (2.5 min upwards). The intensity-velocity correlation is characteristic of a standing compressional wave.
3. Intensity cinefilms at Hα line centre show in places a horizontal drift of the chromospheric granulation pattern at about 12 km s^-1 without any accompanying vertical velocity fluctuations. It is not known whether this is due to a gas stream at sonic velocities, or to a horizontally propagating sound wave.

The Alfvén wave system is shown to make a significant contribution to coronal heating. Whether the velocity fluctuations in the chromospheric granulation also make an important contribution depends on whether there are upwardly propagating or standing waves; this is not yet established despite the intensity-velocity correlation.     

The structure of steady detonation waves in Type Ia supernovae: pathological detonations in C–O cores

The structure of steady, one-dimensional detonation waves in C–O is investigated for initial densities in the range 2×10⁷ to 1×10⁹ g cm⁻³. At these and greater densities, the self-supporting detonation wave is of the pathological type. For such waves the detonation speed is an eigenvalue of the steady equations, and the reaction zone contains an internal frozen sonic point where the thermicity vanishes. The self-supporting flow downstream of this singular point is supersonic, and is very different from that in supported (overdriven) detonations. A method for determining the structure of pathological detonation waves is described. These waves are examined, and the self-sustaining wave is compared with and contrasted to the supported detonations considered previously by Khokhlov. We show that the thickness of the self-sustaining detonation is a few times the thickness of supported detonations, and that the self-sustaining detonation produces more of the iron-peak and less of the intermediate mass elements than do supported detonations. Implications for the cellular detonation instability are also discussed.     

The two-dimensional structure of thin accretion disks

The two-dimensional structure of a thin accretion disk in the vicinity of a Schwarzschild black hole after passing a marginally stable orbit (r< 3r _g is discussed in terms of the Grad-Shafranov hydrodynamic equation. The accretion disk is shown to be sharply compressed as the sonic surface is approached, so the mass flow here is no longer radial. As a result, the dynamic forces ρ[(v ?)v] _θ , which are equal in magnitude to the pressure gradient ? _θ P on the sonic surface, become significant in vertical balance. Therefore, the disk thickness in the supersonic region (and, in particular, near the black-hole horizon) may be assumed to be determined not by the pressure gradient but by the shape of ballistic trajectories.     

Hydrodynamic instability of convectively unstable atmospheres in shear flow

Results are presented concerning the interaction between regions of convectively unstable fluid, bounded above and below by stable fluid, with a basic horizontal flow field, sheared in a vertical direction. The analysis is conveniently based on the definition of the mechanical energy flux associated with wave motion in a stratified compressible fluid, and enables bounds to be placed on the real and complex phase velocities of overstable modes, in addition to some general results on the net upward wave energy flux. It is shown that purely exponentially growing modes (with horizontal wavevectors spanwise to the shear) do not exist. A known sufficient condition for the stability of stable atmospheres is reproduced here with an interesting modification, and details of energy-flux discontinuities at certain singular points of the equations are given. The work is relevant to any astrophysical and geophysical situations in which convectively unstable regions and shear flows are likely to be together present, but the special motivation here is that of describing some aspects of the interaction between supergranular flow and granular convection.