Reconstruction of large-scale structures and acoustic radiation from a turbulent M=0.9 jet using the proper orthogonal decomposition

The Proper Orthogonal Decomposition (POD) uses data to generate an optimal set of basis functions that represent the " energy " of the data, defined by a user-selected norm. This basis is optimal in the sense that a finite number of these modes represent more of the energy than any other set of orthogonal modes. The POD can be seen, on one hand, as a way to define energetic structures in a flow, essentially a generalization of the traditional Fourier-based spectrum to treat data that is inhomogeneous in one or more coordinate directions. But the POD modes are perhaps more useful in quantitatively modeling the dynamics of the flow, via Galerkin projection of the governing equations onto a relatively small number of modes in order to generate a reduced-order model. Here we document the three-dimensional POD modes, based on a varitey of norms, of a round, subsonic, turbulent jet (with Mach number 0.9 and Reynolds number 3600) that was recently computed with well-validated DNS[1]. Of special interest is the three-dimensional structure of the POD modes that involve all near field quantities (velocities and thermodynamic variables), which has not been possible to measure directly. Instead, experiments have concentrated either on slices of the jet (normal to the flow direction) in which the streamwise velocity alone is used to compute the POD modes (e.g. [2]), or pressure measurements along the streamwise direction at a position just outside the jet (e.g. [3]). We investigate the connection between energetic structures (defined with POD) in the near field and the far-field radiated sound. An intriguing question is whether an appropriate norm can be defined that would efficiently represent the sound producing dynamics of the flow, and a long term goal of the present work is to