Delineation and evolution of aerodynamic and acoustic components of pressure in turbulence

To aid in jet noise source identification, several studies have attempted to isolate the propagating component of pressure from that which convects with structures. While the former contributes to farfield sound of the jet (acoustic pressure), the latter decays rapidly in the nearfield (aerodynamic or hydrodynamic pressure). Fourier- and wavelet-analyses usually used to split pressure in this manner rely on various pre-defined parameters such as wave-speed and statistics of coherent events, which introduce ambiguity in the analysis. The availability of accurate spatio-temporal data from high-fidelity simulations offers an opportunity to perform this separation in a more rigorous manner. We propose a first-principle-based approach predicated on the availability of pure acoustic and hydrodynamic components of fluctuations in any turbulent medium. Specifically, the momentum potential theory is extended to derive Poisson equations which separate the acoustic and hydrodynamic components of pressure from the momentum equations. The splitting is successfully applied to a turbulent jet and yields insights into the spatio-temporal segregation that prevails among the constituent components of pressure fluctuations.