The interaction of an isotropic field of acoustic waves with a shock wave

Moore's (1954) inviscid linear analysis of the interaction of a shock wave with a plane acoustic wave is evaluated by comparison to computation. The analysis is then extended to study the interaction of an isotropic field of acoustic waves with a normal shock wave. The evolution of fluctuating kinetic energy, sound level and thermodynamic fluctuations across the shock wave are examined in detail. The interaction of acoustic fluctuations with the shock is notably different from that of vortical fluctuations. The kinetic energy of the acoustic fluctuations decreases across the shock wave for Mach numbers between 1.25 and 1.8. For Mach numbers exceeding 3, the kinetic energy amplifies by levels that significantly exceed those found in the interaction of vortical fluctuations with the shock. Upon interacting with the shock wave, the acoustic waves generate vortical fluctuations whose contribution to the far-field kinetic energy increases with increasing Mach number. The level of sound increases across the shock wave. The rise in the sound pressure level across the shock varies from 5 to 20 dB for Mach number varying from 1.5 to 5. The fluctuations behind the shock wave are nearly isentropic for Mach number less than 1.5, beyond which the generation of entropy fluctuations becomes significant.