Development of an extended proper orthogonal decomposition and its application to a time periodically forced plane mixing layer

Two extensions of the classical proper orthogonal decomposition (POD) methodology exposited by Lumley for turbulent flows are presented. First, the extended POD (EPOD) can deal with flows lacking statistical stationarity by summing the velocity correlations of an ensemble of time series. Thus it reduces to the classical POD for a statistically stationary flow, and to the ‘‘snapshot’’ of Sirovich for data from a single instant in each realization of an ensemble. Second, the EPOD can deal with flows having one or more length scales exceeding the spatial range over which simultaneous measurements can be made, by generating composite modes using nonsimultaneous, spatially overlapping data. Both new capabilities have been exercised by applying the EPOD to the streamwise velocity component measured by a cross-stream hot-wire rake in an anharmonically forced turbulent plane mixing layer that is not statistically stationary, and is statistically homogeneous in only one direction. It is discovered that as few as three one-dimensional modes are capable of capturing as much as 78% of the ‘‘action’’ in data from ten wires in a cross-stream rake.