Sound source analysis based on the constrained acoustic resolvent in a physical forcing space

The linearized inhomogeneous Euler (LIE) equation, originated from the generalized acoustic analogy theory, demonstrates that there is an exact analogy between the fluctuations occurring in any real flow and the linear inviscid fluctuations about an arbitrary flow produced by appropriate external stress and energy flux perturbations, which can be regarded as an input−output system. By employing a well-defined base flow, acoustic resolvent analysis can be performed based on the LIE equation, where the forcing mode corresponds to the sound source and the response mode to the far-field noise. According to such analyses, one can identify the nominally sound source structures that possess the highest acoustic radiation efficiency, which are optimally enhanced by the LIE system. However, a significant challenge arises from the rarity or even the nonexistence of these structures in actual flows. To address this, we have developed a constrained acoustic resolvent analysis with a physical low-dimensional forcing space, in which the forcing is space-time correlated. This approach can reveal the most significant part of sound source structures within flow fields, which is crucial for economical and efficient noise reduction control design. Then, sound noise analysis based on the constrained acoustic resolvent is applied in a subsonic turbulent jet. The dominant source mechanisms with high acoustic efficiency indicated by the optimal resolvent mode have been identified clearly. The leading forcing modes of constrained acoustic resolvent modes are capable of proposing a low-rank source model to recover the acoustic field. While the generalized acoustic analogy provided mathematical sources rather than true sound sources, we illustrated that the constrained acoustic resolvent is capable of distinguishing the ingredients with strong noise production in the far field and has the potential to develop a more accurate noise model as well as efficient noise control strategies in this framework.