Madhukar Gaur

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.

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.

Thermal effects on weak waves in a radiative magnetogasdynamic media

The singular surface theory has been used to determine the behavior of weak waves under the combined influence of time-dependent gasdynamic, radiation, and electromagnetic fields. The role of thermal radiation and conduction in the growth or decay of a wave has been studied under a quasiequilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative heat-transfer equation. It is shown that there are two distinct modes of wave propagation, namely, a radiation-induced wave and a modified magnetogasdynamic wave. It is observed that a radiation-induced wave decays rapidly and has a negligibly small influence on the gasdynamic field under the nonrelativistic limit, whereas a magnetogasdynamic wave grows into a shock wave under nonlinear steepening effects. Two cases of diverging and converging waves are discussed to answer the question as to when a shock wave appears. 11 references.

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.

Anisotropic propagation of weak discontinuities in flows of thermally conducting and dissociating gases

The object of the present investigation is to study the anisotropic propagation of weak discontinuities in flows of thermally conducting and dissociating gases. The velocity of propagation of the wave frcnt is determined. A set of differential equations governing the growth and decay of weak discontinuities are obtained and solved. It is found 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. It is also observed that the effects of heat conduction and dissociation are to decrease the duration of time by which a weak discontinuity will generate into a shock wave.

Growth and decay of weak disturbances in visco-elastic arteries

SummaryIn non-linear mathematical models of the arterial circulation, the visco-elasticity of the vessel walls has generally been neglected or only taken into account in a highly approximate manner. The object of the present paper is to provide a mathematical model for the propagation of weak disturbances in visco-elastic arteries. A differential equation governing the growth and decay of the waves has been obtained and solved analytically. It is observed that compressive pulses may grow into shock waves. A mathematical model which is based on geometrical and mechanical properties of arteries admits disturbances in the propagating pulses which are not observed in human beings under normal physiological conditions. It is also predicted that visco-elasticity delays the shock wave formation in the model. The shock wave may appear in periphery in the case of aortic insufficiency due to increased pressure at the root of aorta. The corresponding predictions are in much better agreement within vivo measurements.

Similarity solutions of isothermal flows behind a MGD blast wave in an inhomogeneous medium

SummarySelf-similar solutions of isothermal flows behind a cylindrical magnetogasdynamic blast wave have been obtained. A strong cylindrical shock wave generated by a sudden line source explosion in an inhomogeneous medium of electrically conducting gas has been studied. Numerical and analytical treatments have been presented and a uniformly valid distribution of pressure, density and velocity profiles has been determined and the magnetic-field effects on the flow distributions have been investigated. The shock propagation law is determined by extending Whitham’s rule for a MGD flow with infinite electrical conductivity.RiassuntoSi sono ottenute soluzioni autosimili di flussi isotermici dietro un’onda espansiva, magnetogasdinamica, cilindrica. È stata studiata un’onda d’urto forte cilindrica generata da un’improvvisa esplosione a sorgente lineare in un mezzo non omogeneo di un gas elettricamente conduttore. Si presentano trattamenti numerici e analitici e si è determinata una distribuzione uniformemente valida dei profili di pressione, densità e velocità e si sono studiati gli effetti del campo magnetico sulle distribuzioni del flusso. La legge di propagazione dell’urto si determina estendendo la regola di Whitham per un flusso MGD con conduttività elettrica infinita.РезюмеПолучются самоподобные решения для изотермических потоков за цилиндрической магнитогазодимамической ударной. Исследется сильная цилиндческая ударная волна, которая обрзуетсяв резуль↦ате внеапного взрыва линейного истоника в неоднородной среде электрически проводящего газа. Проводятся численное и аналитическое рассмотрение. Определяжтся распредение давления, профили плотности и скорости. йсследуется влияние магнитного поля на распредение потока. Определется закон распространения ударной волны, обобшая правило Витама для магнитогазодинамического потока с бесконечной электрической проводимостью.

The growth and decay of weak waves in relativistic flows of dissociating gases

The propagation of a weak wave in a relativistic flow of a dissociating gas has been studied. The velocity of propagation of a relativistic weak wave has been determined. The fundamental growth equation governing the growth and decay of the wave has been obtained and solved. The relativistic results have been shown in full agreement with earlier results of classical gas dynamics. The problem of breakdown of weak discontinuities has also been solved. The critical time tc is determined when the breakdown of the wave and the consequent formation of a shock wave occur due to nonlinear steepening. It is concluded that there exists a critical amplitude of the wave such that all compressive waves with an initial amplitude greater than the critical one will break down after a finite time tc and a shock‐type discontinuity will be formed, while an initial amplitude less than the critical one will result in a decay of the wave. On the other hand, an expansion wave will always decay and will ultimately be damped out....