Radhe Shyam

Growth and decay of weak discontinuities in radiative gasdynamics

Abstract Growth and decay properties of weak discontinuities headed by wave fronts of arbitrary shape in three dimensions are investigated in a thermally radiating inviscid gas flow. The effects of radiative transfer are treated by the use of a general differential approximation for a grey gas of arbitrary opacity including effects of radiative flux, pressure and energy density. 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 radiation induced waves. In contrast to the radiation induced waves, the nonlinearity in the governing equations plays an important role in the interplay of damping and steepening tendencies of a modified gasdynamic wave. An explicit criterion for the growth and decay of a modified gasdynamic wave along bicharacteristics curve in the characteristic manifold of the governing differential equations is given and the special reference is made of diverging and converging waves. It is shown that there is a special case of a compressive converging wave for which the stabilizing influences of thermal radiation and the wave front curvature are not strong enough to overcome the tendency of the wave to grow into a shock.

Steepening of waves in radiative magnetohydrodynamics

Abstract Singular surface theory is used to determine the modes of wave propagation and development of discontinuities at planar and cylindrical wave fronts. It is investigated as to how the effects of thermal radiation and magnetic field strength influence the steepening and flattening of wave fronts. Although the effect of magnetic field, whether axial or azimuthal, is to increase the shock formation distance, it, unlike the effect of thermal radiation, cannot offset the tendency of a compression wave-head, carrying a jump discontinuity (no matter how weak initially), to grow into a shock wave after a finite running length. In an optically thick gas with negligible radiation pressure and energy, an increase in the radiative flux reduces the shock formation distance; this is in contrast to the corresponding result for an optically thin gas where an increase in the radiative flux causes shock formation distance to increase. However, numerical calculations show that in a temperature range 9 × 10 4 T 5 , the combined effect of radiation pressure, energy and flux is to delay the formation of a shock wave. It is found that the decaying of expansion waves is enhanced (slowed down) due to the presence of thermal radiation (magnetic field).

Behaviour of a Discontinuity at the Wave-Head Propagating Through a Relaxing Gas

SummaryThe rate of amplification of a discontinuity in the velocity gradient is evaluated at the wave-head in a spatially uniform but time evolving flow of a relaxing gas. The paper investigates the effects of relaxation (present in the flow) and the initial wave front curvature on the growth and decay behaviour of waves in the thermodynamical state of weak or strong equilibrium.

Nonlinear breaking of waves in an electrically conducting and radiating gas

The effects of radiative transfer are treated by the use of a differential approximation which is valid over the entire optical depth range from the transparent limit to the optically thick limit. The singular surface theory is used to determine the modes of wave propagation and to evaluate the behaviour at the wave head. It is shown that there are two modes of wave propagation namely (i) the radiation induced waves which are always damped, and (ii) the modified magnetogasdynamic waves which break at the wave front if the initial discontinuity is sufficiently strong. The effects of thermal radiation, the magnetic field intensity, the finite electrical conductivity and the initial wave front curvature on the non-linear breaking of modified magnetogasdynamic waves are discussed.ZusammenfassungDer Einfluß der Strahlung wird mit Hilfe von Differential-Näherungen behandelt, die im ganzen Bereich von optischen Tiefen Gültigkeit haben, von der Transparenz bis zur optisch dicken Grenze. Die Theorie singulärer Flächen wird benützt um die Wellenausbreitung und das Verhalten an der Wellenfront zu behandeln. Es wird gezeigt, daß es zwei Formen von Wellenausbreitung gibt, nämlich (i) Wellen erzeugt durch Strahlung, die immer gedämpft sind, und (ii) die modifizierte magnetogasdynamische Welle, die an der Front immer bricht, wenn die ursprüngliche Diskontinuität stark genug ist. Es werden die Einflüsse der Wärmestrahlung, der magnetischen Feldstärke, der endlichen elektrischen Leitfähigkeit und der ursprünglichen Wellenkrümmung auf die nicht-lineare Frontbildung untersucht.

Propagation of weak discontinuities along the bicharacteristic curves in a vibrationally relaxing gas

Abstract The transport equations representing the rate of change of discontinuities in the normal derivatives of flow parameters are obtained along bicharacteristic curves in the characteristic manifold of the differential equations governing the flow of a vibrationally relaxing gas, an explicit criterion for the growth and decay of weak discontinuities along bicharacteristics is given and the specialization is made to the waves of plane, cylindrical and spherical geometry. It is investigated as to how the effects of vibrational relaxation, the magnitude of the initial discontinuity, the initial curvature of the wave front, and the upstream flow Mach number will influence the growth and decay properties of the wave front.

On the breakdown of wave fronts of characteristics in an ideal dissociating gas

Abstract Using the method of characteristics, the problem of breaking or non-breaking of waves is studied in a plane cylindrically or spherically symmetric flow of an ideal dissociating gas. It is investigated as to how the effects of dissociation and that of the wave front curvature influence the breaking or non-breaking of waves. In a symmetrical converging gas motion a remarkable difference between the behaviours of cylindrical and spherical waves is discovered.

The onset of converging and diverging shock waves in non-equilibrium gas flows

Abstract In this work, the effects of thermodynamical influences and that of wave front curvature on the propagation of finite amplitude waves of arbitrary shape and their consequent formation into shock waves are examined.

On flows with vibrational relaxation behind an attached shock wave

Abstract The flow conditions are represented by an oblique shock attached to the vertex of a straight edged wedge, placed symmetrically with respect to a uniform supersonic flow in front, so that the flow after the shcok is along the wedge surface. The curvature of the attached shock wave, and the flow variable gradients at the wedge tip caused by non-equilibrium vibrational effects are determined for a steady two-dimensional flow of a vibrationally relaxing gas. A relation between the curvature of the shock and that of the stream line is obtained at the wedge-tip. The variation of entropy and an expression for the vorticity generated by the shock towards down-stream flow are determined. Calculations have been carried out for the shock curvature and flow variable gradients for a wide range of wedge angle and the up-stream flow Mach number.

Propagation of discontinuities along bicharacteristics in the unsteady flow of a relaxing gas

Growth and decay of weak discontinuities headed by wave front of arbitrary shape in three dimensions are investigated in an unsteady flow of a relaxing gas. 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 plays an important role in the interplay of damping and steepening tendencies of the wave. An explicit criterion for the growth and decay of weak discontinuities along bicharacteristic curves in the characteristic manifold of the governing differential equations is given and special reference is made of diverging and converging waves under different thermodynamical situations. It is shown that there is a special case of a compressive converging wave, irrespective of the thermodynamical state whether weak or strong, in which the effects of thermodynamical influences and that of wave front curvature are unable to overcome the tendency of the wave to grow into a shock.

Growth of discontinuities in fluids with internal relaxation

The growth equation for weak discontinuities headed by wave fronts of arbitrary shape in a relaxing gas flow is derived along the orthogonal trajectories of the wave fronts. An explicit criteria for the growth and decay of weak discontinuities along their orthogonal trajectories is given. It is concluded that the internal relaxation processes in the flow as well as the wave front curvature both have a stabilizing effect on the tendency of the wave surface to grow into a shock in the sense that they cause the shock formation time to increase.