Proper Orthogonal Decomposition of Turbulent Flows for Aeroacoustic and Hydroacoustic Applications

This paper describes the use of proper orthogonal decomposition (POD) for problems in which sound radiation is caused by turbulent flow interacting with rigid surfaces. For a complete solution the statistics of the turbulent velocity fluctuations must be defined, and it is customary to base these on spectral analysis. This paper will describe how proper orthogonal modes provide a better approach than spectral analysis for inhomogeneous turbulent flows. One of the additional advantages of POD is that sound radiation problems may be analyzed in the time domain and this may prove useful in rotor noise applications where time-domain calculations are frequently used. For flows that are stationary in time or homogeneous in at least one direction, it will be shown that there are advantages in using a combination of POD and a linear stochastic estimator to describe the flow. This provides a decomposition of the two-point cross-correlation function of the turbulence that requires fewer modes than POD.