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

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.     

Growth and decay of weak discontinuities in radiative gasdynamics

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.     

On flows with vibrational relaxation behind an attached shock wave

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.     

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

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.