Spherical shock wave propagation in self-gravitating stars

The problem of shock wave propagation in a heat-conducting and self-gravitating medium has been studied. The shock is strong enough so that the ambient gas pressure can be neglected. The variation of velocity, density, temperature, and mass distributions behind the shock have been obtained from a numerical solution of similarity equations involved.     

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.     

Wave propagation in the photosphere

Using a 32 minutes sequence of observation, brightness and velocity fluctuations in the wings of the Mgi line at 5172.7 Å and Fe ii line at 5197.578 Å are analysed. The analysis of phase shifts and amplitude ratios leads to the following conclusions:

Wave propagation in the warm plasma and the spectrum of the solar radio bursts

The frequency bands of noise storms and type I-bursts as well as of type IVdm-bursts are shown to be in accordance with the consequences of a recently proposed mechanism (Mollwo, 1970). An explanation results of the observed spectral minimum near 600 MHz and interpretations are supposed of some features of type III- and of type IVmA-bursts. The magnetic field strength over active regions in two corona levels is deduced, too. The discussion leads to a conception of the corona parameters in the level of type IV-bursts which suggests an origin of these bursts by absolute instability of space charge waves.     

Wave propagation in intense flux tubes

The nature of non-adiabatic wave propagation in a slender magnetic flux tube is explored. The results of the theory are compared with the observations of Giovanelli et al. (1978), and found to be in general agreement. Those observations, of tubes in the photosphere-chromosphere, show outwardly propagating waves, with periods of 300 s, which take some 19 s to propagate from one level of line formation to another level higher in the atmosphere. In sharp contrast to this, is the time of 7 s for a similar disturbance outside the tube to propagate between the same two levels of line formation, estimated to be some 600 km apart in the field-free atmosphere. It is argued that the sharply contrasting propagation times for the tube and its environment is principally due to the elasticity of the tube and its subsequent propensity for propagation. A non-adiabatic disturbance may be essentially propagating within the tube but essentially non-propagating outside, with considerably slower phase speeds thus arising inside the tube. The theory suggests that the observed disturbances are non-adiabatic, acoustic-gravity waves channelled along a magnetic flux tube and modulated by external pressure variations.     

Wave propagation in a magnetic cylinder

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvénic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvénic-type, oscillations arise only in high density (strictly, low Alfvén velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.     

Similarity solution of the propagation of spherical shock waves in a magnetogasdynamic self-gravitating system

The self-similar model of propagation of spherical strong shock waves into non-uniform stellar atmosphere under self-gravitation and non-uniform magnetic field is investigated. The disturbances are headed by a shock surface of variable strength. Gas is assumed to be grey and opaque and the shock tobe transparent.     

Wave propagation in a magnetically structured atmosphere

The solar atmosphere, from the photosphere to the corona, is structured by the presence of magnetic fields. We consider the nature of such inhomogeneity and emphasis that the usual picture of hydromagnetic wave propagation in a uniform medium may be misleading if applied to a structured field. We investigate the occurrence of magnetoacoustic surface waves at a single magnetic interface and consider in detail the case where one side of the interface is field-free. For such an interface, a slow surface wave can always propagate. In addition, a fast surface wave may propagate if the field-free medium is warmer than the magnetic atmosphere.     

Wave propagation in a magnetically structured atmosphere

The propagation of waves in a magnetic slab embedded in a magnetic environment is investigated. The possible modes of propagation are examined from the general dispersion relation, both analytically and numerically, for disturbances which are evanescent in the environment. Approximate dispersion relations governing propagation in a slender slab of field are derived both from the general dispersion relation and from an application of the slender flux tube approximation.Several different situations, representative of both photospheric and coronal conditions, are considered. In general, the structures are found to support both fast and slow, body and surface, waves. Under coronal conditions, for two dimensional propagation, disturbances propagate as fast and slow body waves. The fast body waves are analogous to the ducted shear waves of seismology (Love waves).     

Wave propagation in the magnetosphere of Jupiter

The magnetosphere of Jupiter has been the subject of extensive research in recent years due to its detectable radio emissions. Observations in the decimetric radio band have been particular helpful in ascertaining the general shape of the Jovian magnetic field, which is currently believed to be a dipole with minor perturbations. Although there is no direct evidence for thermal plasma in the magnetosphere of Jupiter, theoretical considerations about the physical processes that must occur in the ionosphere and magnetosphere surrounding Jupiter have lead to estimates of the thermal plasma distribution. These models of the Jovian magnetic field and thermal plasma distribution, specify the characteristic plasma and cyclotron frequencies in the magnetosplasma and thereby provide a basis for estimating thelocal electromagnetic and hydromagnetic noise around Jupiter. Spatial analogs of the well-known Clemmow-Mullaly-Allis (CMA) diagrams have been constructed to identify the loci of electron and ion resonances and cutoffs for the different field and plasma models. Regions of reflection, mode coupling, and probable amplification are readily identified. The corresponding radio noise properties may be estimated qualitatively on the basis of these various electromagnetic and hydromagnetic wave mode regions. Frequency bands and regions of intense natural noise may be estimated. On the basis of the models considered, the radio noise properties around Jupiter are quite different from those encountered in the magnetosphere around the Earth. Wave particle interactions are largely confined to the immediate vicinity of the zenographic equatorial plane and guided propagation from one hemisphere to the other apparently does not occur, except for hydromagnetic modes of propagation. The characteristics of these local signals are indicative of the physical processes occurring in the Jovian magnetosphere. Thus, as a remote sensing tool, their observation will be a vital asset in the exploration of Jupiter.     

Wave propagation in the quiet solar chromosphere

In order to precise previous results about wave propagation in the quiet chromosphere (N. Mein and P. Mein, 1976), we study the behaviour of Doppler shifts and intensity fluctuations in 3 lines of Ca ii. We use the same observation as in our previous work, that is to say a sequence of spectra lasting 27 mn, taken at Sacramento Peak Observatory solar tower. Results can be summarized as follows:

1. Phase-lag between intensity fluctuations and dopplershifts is always near 90° in the Ca ii lines, even for frequencies as high as 15 mHz, and whatever is the location in the chromospheric network.
2. Magneto-acoustic waves propagating vertically in a vertical or horizontal magnetic field could account for the observations only if they were, on one hand reflected in the upper atmosphere, on the other hand propagating with a very high sound or Alfvén speed. The lower limit for the speed (70 km s^-1) does not seem to be realistic. Oblique waves could be investigated for better agreement.

     

Effect of azimuthal magnetic field on the propagation of cylindrical shock waves in self-gravitating gas

A propagation of diverging cylindrical shock in a self-gravitating gas, having an initial density and azimuthal magnetic field distributions variable, has been studied for the two cases (i) when the shock is weak and (ii) when it is strong. Analytical relations for shock velocity and shock strength have been obtained. Lastly, the expressions for the pressure, the density and the particle velocity immediately behind the shock have been also obtained for both cases.     

Effect of overtaking disturbances on the propagation of spherical shock wave through self-gravitating gas

Effect of overtaking disturbances on the propagation of a spherical shock wave in self gravitating gas has been studied by the technique developed by the first author [Mod. Meas. Cont. B,46(4), 1 (1992)]. The analytical expressions for modified shock velocity and shock strength have been obtained for an initial density distribution0 =r ^–w, where is the density at the axis of symmetry andw is a constant; simultaneously, for the two cases viz.; (i) when the shock is strong and ii) when it is weak. The results accomplished here have been compared with those for freely propagation of shock.It is observed that the conclusions arrived at here agree with experimental observations. Finally, the modified expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived from, for both cases.     

Energy dissipation in wave propagation in general-relativistic plasma

Based on a recent communication by the present authors the question of energy dissipation in magnetohydrodynamical waves in an inflating background in general relativity is examined. It is found that the expanding background introduces a sort of dragging force on the propagating wave such that, unlike the Newtonian case, energy gets dissipated as it progresses. This loss in energy having no special-relativistic analogue is, however, not mechanical in nature as in case of an elastic wave. It is also found that the energy loss is model dependent and also depends on the number of dimensions.     

Nonlinear disturbances in self-gravitating media

Using a multiple time-scale method, the weakly nonlinear waves on a self-gravitating incompressible fluid column are investigated. The analysis reveals that near the wavenumberk=k _c , the amplitude modulation of a standing wave can be described by the nonlinear Schrödinger equation with the roles of time and space variables interchanged. The nonlinear cutoff wavenumber, which depends sensitively on initial conditions, can then be derived from the nonlinear Schrödinger equation so obtained. The finite amplitude standing wave is stable against modulation.     

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.     

Magneto-radiative shock wave propagation in a conducting plasma

Similarity solutions describing the flow of a perfect gas behind a spherical and cylindrical shock wave in a magnetic field with radiation heat flux have been investigated. The total energy of the expanding wave has been assumed to remain constant. The solutions, however, are only applicable to a gaseous medium where the undisturbed pressure falls as the inverse square of the distance from the line of explosion.     

Shock waves propagation in the turbulent interplanetary plasma

Effect of turbulence on interplanetary shock waves propagation is considered. It is shown that background turbulence results in the additional shock wave deceleration which may be comparable with the deceleration due to plasma sweeping. The turbulent deceleration is connected with the energy losses due to the strong turbulence amplification behind the moving shock front.