Asymptotical solutions for a vibrationally relaxing gas

Abstract

Using the weakly non‐linear geometrical acoustics theory, we obtain the small amplitude high frequency asymptotic solution to the basic equations governing one dimensional unsteady planar, spherically and cylindrically symmetric flow in a vibrationally relaxing gas with Van der Waals equation of state. The transport equations for the amplitudes of resonantly interacting waves are derived. The evolutionary behavior of non‐resonant wave modes culminating into shock waves is also studied.

First published online: 14 Oct 2010