A unified theory for gas dynamics and aeroacoustics in viscous compressible flows. Part I. Unbounded fluid

This paper presents a deep reflection on the advective wave equations for velocity vector and dilatation discovered in the past decade. We show that these equations can form the theoretical basis of modern gas dynamics, because they dominate not only various complex viscous and heat-conducting gas flows but also their associated longitudinal waves, including aero-generated sound. Current aeroacoustics theory has been developing in a manner quite independently of gas dynamics; it is based on the advective wave equations for thermodynamic variables, say the exact Phillips equation of relative disturbance pressure as a representative one. However, these equations do not cover the fluid flow that generates and propagates sound waves. In using them, one has to assume simplified base-flow models, which we argue is the main theoretical obstacle to identifying sound source and achieving effective noise control. Instead, we show that the Phillips equation and alike is nothing but the first integral of the dilatation equation that also governs the longitudinal part of the flow field. Therefore, we conclude that modern aeroacoustics should merge back into the general unsteady gas dynamics as a special branch of it, with dilatation of multiple sources being a new additional and sharper sound variable.