The growth of discontinuities in a non-equilibrium flow of a relaxing gas

Abstract

The growth and decay properties of first-order discontinuities headed by wave fronts of arbitrary shape in a non-equilibrium gas flow are investigated. Exact predictions of true nonlinear progress of the flow-variable gradients at the wave front are made for both converging and diverging waves. It is found that a compressive wave terminates into a shock only if the magnitude of initial discontinuity associated with a wave exceeds a critical value, except in a special case of converging waves. It is shown that the geometry of the wave front affects the growth properties only indirectly in that the critical value of the initial discontinuity depends on the initial curvature of the wave front. The strength of attenuation induced by geometric factors relative to the growth induced by thermodynamical properties of the gas is investigated. © 1979 Oxford University Press.