On double waves and wave-wave interaction in gasdynamics

Abstract

Special classes of potential isentropic nonstationary flows in two space dimensions are considered. We demonstrate that locally these solutions can be understood as resulting from what we call elastic interaction (since no other waves are produced) of two Riemann waves (simple waves). It appears that this is a generic property of interactions of sound modes in gasdynamics. That is, two non linear (localised) sound waves propagating at any angle can cross each other without producing new waves - similarly as it happens in one space dimension.