Growth and Decay of One-Dimensional Shock Waves in Fluids with Internal State Variables

Abstract

A differential equation is derived relating the density ρ − and the density gradient ρx − behind a shock wave when the region ahead of the wave has always been at equilibrium. The existence of a critical density gradient λ (generally negative) is established: For a compression shock ρ − will increase, decrease, or remain constant according as ρx − is less than, greater than, or equal to λ . λ is shown to be related to the critical amplitude for acceleration waves; an experimental procedure for determining λ as a function of ρ − is given.