Propagation and evolution of waves in a self-gravitating medium

The propagation and evolution of linear waves in a self-gravitating medium are discussed in a comparatively general way. In one special case, the well-known Jeans formula is recovered; in another, an important property of unstable waves in a self-gravitating medium is obtained, namely, the equiphase surfaces of the wave are “frozen” in the moving medium. When the motion of the basic state is one of shear flow (or differential rotation), this property implies that unstable waves would evolve into a quasi-stationary state. This shows that, for a self-gravitating medium, besides the usual non-linear effects, there is a special mechanism within the linear theory which prevents the infinite growth of unstable waves. Possible relation of this effect to the origin of celestial bodies is pointed out.     

Parametric generation of magnetoacoustic-gravity waves in the solar atmosphere

Based on a plane-parallel isothermal solar model atmosphere permeated by a horizontal magnetic field whose strength is proportional to the square root of the plasma density and in the approximation of a specified field for vertically propagating and nonpropagating magnetoacoustic-gravity waves, we consider the nonlinear interaction between the corresponding disturbances, to within quantities of the second order of smallness. We investigate the efficiency of the nonlinear generation of waves at difference and sum frequencies and of an acoustic flow (wind) as a function of the magnetic-field strength and the excitation frequency of the initial disturbances at the lower atmospheric boundary.     

Propagation of plane relativistic shock waves in a slowly moving medium

Similarity solutions for the propagation of plane relativistic shock waves in a slowly moving medium, where the nucleon number density obeys an exponential law ofx/t, is obtained in this paper. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium.     

Propagation of magnetogasdynamic spherical shock waves in an exponential medium

In this paper propagation of magnetogasdynamic spherical shock waves is considered in an exponentially increasing medium. The shock wave moves with variable velocity and the total energy of the wave is variable. It is shown that the magnetic field changes the flow velocity, density and pressure.     

Propagation of magnetogasdynamic spherical shock waves in an exponential decreasing medium

By use of the approximate method of Whitham (1958) the effect of magnetic field is investigated on a point explosion in a medium exihibiting exponential decrease of density and temperature. It has been found that the shock velocity and shock Mach number first decrease, but after a certain distance they start increasing.     

Propagation of spherical shock waves in non-homogeneous medium with idealized magnetic field

By use of the approximate method of Whitham (1958), the propagation of magnetogasdynamic spherical shock waves is considered for adiabatic and isothermal flows in a decreasing density medium. The effect of initial magnetic fields on the shock velocity is discussed; and a comparison made between adiabatic and isothermal cases.     

Propagation of spherical shock waves in an exponential medium with radiation heat flux

In this paper propagation of spherical shock waves with radiation heat flux is considered in an exponentially increasing medium. The shock wave moves with variable velocity and the total energy of the wave is variable. For different values of radiation parameter, the numerical solution has been made and the nature of the field variables are illustrated by the tables.     

On the possibility of heating of local solar chromospheric regions by magnetoacoustic-gravity waves in a thin flux tube

The response of an isothermal atmosphere of a thin vertical magnetic flux tube to the presence of an acoustic-gravity wave field in the external medium is considered. The Laplace transform method is used to solve a problem with initial conditions. The structure of the solution for disturbances in the tube is a superposition of forced oscillations at the source frequency and oscillations decaying as ～ t ^?3/2 (the so-called wave wake). Both components are analogues of the corresponding disturbances in an external medium with a modified amplitude. The excitation under consideration is shown to be effective in the ranges of external oscillation frequencies 0 mHz ≤ v ≤ 3.3 mHz and v ≥ 6.5 mHz. The time-averaged energy flux density for high-frequency magnetoacoustic-gravity waves in the tube is estimated to be ∝ 3.0 × 10⁷ erg cm^?2 s^?1, a value of the same order of magnitude as that required for heating local regions in the solar chromosphere, ∝ 10⁷ erg cm^?2 s^?1.     

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.     

Propagation of Alfven waves in a non-uniform plasma stream

The propagation of the Alfven waves in a plasma stream with a non-uniform density distribution is considered. It is shown that the density inhomogeneity will cause self-scattering of the wave. A longitudinal magnetic field component will be generated and part of the energy of the wave will propagate in directions deviating from the given mean magnetic field. Thus, to explain certain observed features of the solar wind, it is not necessary to appeal to a mixture of Alfvenic and magnetosonic modes.     

Propagation of spiral density waves in a magneto-active disk

The propagation of spiral density waves in a differentially rotating, self-gravitating, magnetoactive and highly flattened disk is investigated by using the asymptotic theory for tightly wound spirals developed by Lin and his collaborators. We adopt the continuum fluid model as the primary basis, and our treatment will be largely analytical. The disk plasma is studied in the frozen field approximation and inhomogenceous magnetic fields in the plane of the disk are considered in detail.In a differentially rotating disk with strong magnetic fields, the field lines will be considerably distorted and the mutual influence of magnetic fields and differential rotation is by no means obvious.In this paper we present a new asymptotic dispersion relation for tightly wound spiral density waves with magnetic fields along the spiral armsB (r). The effects of the magnetic fields lead to such terms likek ²(a ² +V _A ² ), wherek is the wave number,a represents the speed of sound,V _A = (B ²/4)^1/2 is the Alfvén speed,B denotes the field strength, and is the plasma density. These terms depict the well-known magnetoacoustic waves and could have been anticipated without a detailed computation. However the interaction of magnetic fields and differential rotation may give rise to other significant terms which are not so easy to foresee.We also present a more exact local dispersion relation by using the WKB approximation and study the effects of magnetic fields on the growth rate through the parametersQ andJ defined in the literature.Although the effects of the magnetic fields are rather insignificant for applications to Galactic dynamics, the effects of the magnetic fields are important for applications to star formation and problems related to the solar nebula.     

Propagation of cylindrical shock waves in magnetogasdynamics

Using a well-known similarity method, different aspects of cylindrical shock waves in magnetogasdynamics are investigated. Weak and strong shocks have been discussed in strong magnetic field. Combined effects of both the components of magnetic field on flow variables are studied.     

Propagation of blast waves in Roche model

A non-similarity solution for propagation of magnetogasdynamic blast waves in Roche model is obtained. The density outside the central core varies according to some inverse power of distance from the centre of explosion. The strength of the shock surface heading the disturbance as well as the total energy of the wave vary with time.