Rishi Ram

The progressive wave approach analyzing the decay of a sawtooth profile in magnetogasdynamics

An asymptotic approach is used to analyze the main features of weakly nonlinear waves propagating through an electrically conducting gas permeated by a transverse magnetic field. The analysis leads to an evolution equation, which characterizes the wave process in the high‐frequency domain. The growth equation for an acceleration front is recovered as a special case. The influence of the magnetic field on the decay behavior of a sawtooth profile, which is headed by a weak shock front and ends with a magnetosonic disturbance, is investigated. A remarkable difference between the plane and cylindrical wave profiles is noted; for instance, when the adiabatic index γ is 2, the field does not affect the decay behavior of plane waves but does affect cylindrical waves.

Effect of radiative heat transfer on the growth and decay of acceleration waves

The propagation of acceleration waves has been studied along the characteristic path by using the characteristics of the governing quasilinear system as the reference coordinate system. It is shown that a linear solution in the characteristic plane can exhibit non-linear behaviour in the physical plane. As an application of the theory the point is determined where the wave will break down, provided the breaking occurs at the wave front. It is investigated as for how the radiative heat transfer effects under optically thin limit will influence the process of steepening or flattening of acceleration waves with planar, cylindrical and spherical symmetry. The critical time is obtained when all the characteristics will pile up at the wave front to form a shock wave. The critical amplitude of the initial disturbance has been determined such that any compressive disturbance with an initial amplitude greater than the critical one always terminates into a shock wave, while an initial amplitude less than the critical one results in a decay of the disturbance. The radiative heat transfer effects delay the formation of a shock wave and has a stabilizing effect in the sense that not all compressive acceleration waves will grow into shock waves. A non-linear steepening and a radiative heat transfer provide a particular answer to the substantial question as for when a shock wave will be formed.

The growth and decay of sonic waves in a radiating gas at high temperature

The propagation of a sonic discontinuity in an optically thick gray gas at temperature 105°K or higher has been studied. The effects of radiation pressure and radiation energy density have been taken into account, while the profiles structured by radiant heat transfer are imbedded in the discontinuities under high temperature conditions of an optically thick medium. When the sonic discontinuity is propagating into a gas at rest, its velocity of propagation is found to be a constant which is the effective speed of sound in a radiating gas. The fundamental differential equations governing the growth of the sonic discontinuity are obtained and solved. It is concluded that if the sonic discontinuity is a compressive wave of order 1, then it terminates into a shock wave after a critical timetc which has been determined. But on the other hand, when the sonic discontinuity is an expansion wave of order 1, then it will decay and will vanish ultimately. Particular cases of interest have been studied in details.ZusammenfassungEs wird die Ausbreitung einer akustischen Diskontinuität in einem optisch dicken grauen Gas untersucht, bei einer Temperatur von 105°K und darüber. Die Effekte des Strahlungsdruckes und der Strahlungs-Energiedichte sind berücksichtigt worden. Die Profile, deren Struktur durch Strahlung bestimmt wird, werden in den Diskontinuitäten eingepasst unter der Bedingung hoher Temperaturen eines optisch dicken Mediums. Wenn die akustische Diskontinuität sich in einem ruhenden Gas ausbreitet, ist ihre Ausbreitungsgeschwindigkeit eine Konstante, nämlich die effektive Schallgeschwindigkeit des strahlenden Gases. Die grundlegenden Differentialgleichungen, welche das Wachstum der Diskontinuität bestimmen, werden aufgestellt und gelöst. Es wird gezeigt, dass wenn die akustische Diskontinuität von einer Druckwelle der Ordnung 1 gebildet wird, dann entwickelt sie sich in eine Stosswelle im Laufe einer kritischen Zeittc, die bestimmt worden ist. Andererseits wird eine akustische Expansionswelle der Ordnung 1 abklingen und schliesslich verschwinden. Besondere Fälle wurden ausführlich untersucht.

Flow pattern induced by a piston impulsively moving in a perfectly conducting inviscid radiating gas

A self‐similar method is used to study numerically the flow pattern resulting from the impulsive motion of a plane and a cylindrical piston through a perfectly conducting inviscid radiating gas permeated by a transverse magnetic field. The effects of thermal radiation are treated by the differential approximation to the radiative transfer equation. Numerical solutions in the region between the shock and the piston are presented for the cases of general opacity and the transparent limit. The influence of thermal radiation, the magnetic field strength, and the adiabatic heat exponent on the flow pattern for various cases are assessed. The general behavior of the velocity and density distribution remains essentially unaffected by the interaction between the radiative and magnetogasdynamic phenomena. However, the pressure profiles are greatly affected by the interaction; the effect of the magnetic interation is to diminish the effects of radiative transfer.

The growth and decay of sonic waves in dissociating gases

The propagation of sonic waves through dissociating gases has been discussed. The velocity of propagation is determined and it is found that the weak disturbances in dissociating gases propagate with the effective velocity of sound relative to the gas flow. The fundamental differential equations governing the growth and decay of sonic waves are obtained and solved for various forms of wavefronts. It is concluded that if the sonic wave is a compressive wave of order 1, then it terminates into a shock wave after a critical timetc which has been determined. But on the other hand if it is a rarefaction wave, it will continuously decay and will be damped out ultimately. It is also shown that the dissociative effects are to decrease the critical timetc. In the case of a rarefaction wave the effects of dissociation will cause more rapid damping effects.

Radiative heat-transfer effects on the propagation of pressure shocks

Abstract The propagation of a pressure shock has been studied by taking into account the effects of radiative heat transfer. The velocity of propagation of the pressure shock has been determined and its variation with the strength of the shock is computed. It is found that the velocity of propagation of the pressure shock decreases continuously with the decrease of its strength during propagation till the pressure discontinuity vanishes ultimately. The effects of radiative heat transfer will slow down the rate of decrease of the velocity of propagation. A differential equation governing the variations of the strength of the pressure shock during propagation has been determined and solved numerically. The numerical results show that the strength of the pressure shock will continuously decrease till the pressure discontinuity vanishes ultimately. The radiative heat-transfer effects will slow down the rate of decrease in the strength of the pressure shock. The results of Thomas are recovered as a particular case.

Propagation of weak MHD discontinuities in an optically thin medium

The object of the present paper is to study the propagation of weak MHD discontinuities in an optically thin medium. The growth equation governing the growth and decay of MHD discontinuities and the behaviour of their amplitude has been studied. It is observed that expansion waves decay exponentially, while compressive waves may grow into shock waves. A critical value of the amplitude of compressive waves is determined such that all waves with initial amplitude greater than the critical one will grow into shock waves, while those with amplitudes less than the critical one will decay out. The critical time for the formation of shock waves has also been determined.

On the breakdown of acceleration waves in dissociating gas flows

The present paper is devoted to the study of characteristic solution in the neighbourhood of the leading frozen characteristics in dissociating gas flows. It is found that at the cusp of the envelope of intersecting forward characteristics there occurs a breakdown of the wave after a finite critical timeto. It is observed that there exists a critical value of the initial amplitude of the wave such that all compressive waves with an initial amplitude greater than the critical one will terminate into a shock wave due to non-linear steepening while an initial amplitude less than the critical one will result in a continuous decay. It is also concluded that the breakdown point moves forward along the leading characteristics due to dissociation effects.

The relativistic theory of weak discontinuities in high temperature phenomena

Abstract A relativistic theory of the propagation of weak discontinuities in an optically thick medium at temperature 10 50 K or higher is presented. The effects of radiation pressure and radiation energy density have been taken into account, while the profiles structured by radiant heat transfer are assumed imbedded in the discontinuities. The velocity of propagation of a relativistic weak discontinuity has been determined. The fundamental growth equation governing the growth and decay of a relativistic weak wave has been obtained and solved. The relativistic results are shown to be in full agreement with the earlier results of classical gasdynamics. The problem of breakdown of weak waves and the consequent formation of shock waves has also been studied and a finite critical time t c is determined when a weak wave will terminate into a shock wave due to nonlinear steepening. A critical wave amplitude is determined, which provides a critical line for the decay and growth of a weak discontinuity in a relativistic flow referred to an instantaneous rest frame. The local and global behaviour of the wave amplitude is also examined.

On the Growth and Decay of Discontinuities in Relativistic Magnetogasdynamics

The modes of propagation of weak MHD shocks in relativistic fluids have been determined. The fundamental growth equation governing the growth and decay of a weak MHD wave has been obtained and solved under the assumption that the wave is propagating into a uniform medium at rest in the presence of a transverse magnetic field. The relativistic results are shown to be in full agreement with earlier results of classical magnetogasdynamics. The qualitative behaviour of the time-dependent wave amplitude of propagating weak MHD wave fronts has been studied. The problem of breakdown of weakwave solutions is studied and the consequent formation of shock waves has been discussed. A finite critical time tc is determined when a weak wave will terminate into a shock wave due to non-linear steepening. It is also concluded that the relativistic effects somewhat delay the focusing phenomenon in spite of the quasilinear hyperbolic nature of the system of basic equations.