Phase Proper Orthogonal Decomposition of numerical data

We present a Proper Orthogonal Decomposition (POD) technique for describing the four-dimensional (spatial and temporal) behavior of unsteady turbulent flow. We name this technique Phase Proper Orthogonal Decomposition (Phase POD), which does not assume steady or periodic flow. As Phase POD includes all temporal-spatial information in the modes, purely spatial POD[1] and Spectral POD[2] are special cases of Phase POD. The modes of Phase POD will have the energy optimality including the temporal properties. We illustrate the method on an example of a unsteady cavity flow.