A note on the behaviour of finite amplitude waves in a radiating gas

The behavior of weak discontinuities in a radiating inviscid grey gas of arbitrary opacity is investigated analytically, modifying the equations of Sharma et al. (1981) to account for the unsteady behavior of the flow ahead of the discontinuity surface. It is found that the growth equation reduces to a Bernoulli equation along the bicharacteristic curves. For an expansion wave front (where the discontinuity lambda has an initial value at the wave head greater than zero), shock formation is impossible; for a compression wave front (initial lambda less than zero), a shock can form in a nonzero finite time if lambda exceeds a defined critical value.