Cross-correlation of POD spatial modes for the separation of stochastic turbulence and coherent structures

This article describes a proper-orthogonal-decomposition (POD) based methodology proposed for the identification and separation of coherent and turbulent velocity fluctuations. Typically, POD filtering requires assumptions to be made on the cumulative energy content of coherent modes and can therefore exclude smaller, but important contributions from lower energy modes. This work introduces a suggested new metric to consider in the selection of POD modes to be included in a reconstruction of coherent and turbulent features. Cross-correlation of POD spatial modes derived from independent samples is used to identify modes descriptive of either coherent (high-correlation) or incoherent (low-correlation) features. The technique is demonstrated through application to a cylinder in cross-flow allowing appropriate analysis to be carried out on the coherent and turbulent velocity fields separately. This approach allows identification of coherent motions associated with cross-flow transport and vortex shedding, such as integral length scales. Turbulent flow characteristics may be analysed independently from the coherent motions, allowing for the extraction of properties such as turbulent length scale.