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.