The Conditions Necessary for Discontinuous Motion in Gases

Abstract

The possibility of the propagation of a surface of discontinuity in a gas was first considered by Stokes* in his paper “On a Difficulty in the Theory of Sound.” This paper begins with a physical interpretation of Poisson’s integral of the equation of motion of a gas in one dimension. The integral in question is w = f{z - (a + w)t}; and it represents a disturbance of finite amplitude moving in a gas for which the velocity of propagation of an infinitesimal disturbance is a; w is the velocity of the gas in the direction of the axis z. It is shown that the parts of the waves in which the velocity of the gas is w travel forward with a velocity a + w, and that there is in consequence a tendency for the crests to catch up the troughs. After a certain time, and at a certain point in space, the value of ∂w/∂z will become negatively infinite; a discontinuity will then occur, and Poisson’s integral will cease to apply.