Equations for direct numerical simulation of sound propagation in a moving atmosphere

Most previous analytical and numerical studies of sound propagation in a moving atmosphere have been based on wave equations for the sound pressure and on various parabolic approximations to the wave equations. However, these equations cannot be used as starting equations for recently proposed direct numerical simulation (DNS) of sound propagation outdoor since such starting equations should be first-order differential equations with respect to time. In the present paper, we derive two closed sets of the first-order differential equations for the sound pressure and fluctuations in medium velocity and density due to a propagating sound wave. These sets can be used as starting equations for DNS of sound propagation in a moving atmosphere. The ranges of applicability of these sets are studied by comparing them with the equations for the sound pressure used previously. Note that both sets can also be employed for analytical studies of sound propagation in a moving atmosphere. Examples of the use of these sets for DNS and analytical studies of sound propagation in a moving atmosphere are presented. [Work partially supported by a DoD High-Performance Computing Modernization Office grant and U.S. Army Research Office Grant No. DAAG19-01-1-0640.]