A unified theory for gas dynamics and aeroacoustics in viscous compressible flows. Part II. Sources on solid boundary

This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow, of which aeroacoustics will naturally be a special branch. As a continuation of Part I. Unbounded fluid (Mao et al., 2022), this paper studies the source of longitudinal field at solid boundary, caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes. We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless P and temperature T. The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface. We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound, and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur “symmetrically” at the same level, but appears along a zigzag route. At the first level, it is the pressure gradient that generates vorticity unidirectionally; while at the second level, it is the vorticity that generates dilatation unidirectionally. [Figure not available: see fulltext.]