Evolution of weak discontinuities in the unsteady flow of thermally conducting dissociating gases

The time evolution of the velocity-gradient discontinuity (lambda) in the unsteady flow of a thermally conducting gas is investigated analytically. The analysis of Verma and Kumar (1981) is shown to be incorrect, both in its inital framework and in its solutions. The correct basic equations of continuity, momentum, and energy are set forth, and a singular moving surface is introduced. The growth equation for lambda is derived and solved, and the extreme cases of damping out (lambda approaches zero) and shock-wave formation (lambda approaches infinity) are considered. It is pointed out that this analysis is valid for dissociating, chemically reacting, vibrationally relaxiing, or ionizing gases.