On aeroacoustic space-time curvature for certain aerodynamic flows

The research on acoustic metamaterials is probably the most lively research field in classical mechanics since the early achievemnts dating back to 2006. One of the most intriguing and challenging aspects emerged during the last decade deals with the theoretical modeling of the acoustic meta-behavior in presence of a background aerodynamic flow. Indeed, the structure of the equations governing the propagation of an acoustic perturbation in a moving medium is substantially different, due to the effect of the convecive terms, mixing space and time derivatives through the components of the aerodynamic velocity vector field. An effective approach to cope with this aspect relies in the spacetime reinterpretation of the (aero)acoustic equations adopting the analytical tools developed within the framework of the special and general relativity. Indeed, the Minkowskian structure of the equations governing the propagtion of waves in quiescent media turns out to be Lorentzian in presence of a non-uniform background aerodynamic, with the component of the veloicity field acting as space-time-bending elements. The present paper analyses the actual structure of the aeroacoustic spacetime for certain types of flows of interest in many applications. The analysis will take advantage of the existence of analytical solutions to derive the structure of the metric tensor in closed form and make some consideration about the related Ricci's tensor an the corresponding scalar curvarture. The paper will consider potential flows around simple geometries, includig the effect of contact discontinuities (wakes), and potential vortices. The final goal of the research is a deeper understanding of the underlying structure of the acoustic spacetime for those classes of applications where the aerodynamic convections plays a key role, in order to contribute to the disclosure of breakthrough modeling approaches.