Abstract
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.
Highlights
In the field of fluid mechanics, it is possible to obtain detailed, highly-resolved time-space velocity information from both experimental and computational approaches
POD spatial modes are associated with the coherent motions, and which represent flow features representative of turbulence
By the comparison of these independently calculated POD spatial modes from each result set, it may be deduced that those spatial modes that appear in both sets contain coherent flow information
Summary
In the field of fluid mechanics, it is possible to obtain detailed, highly-resolved time-space velocity information from both experimental and computational approaches. Where Ui is velocity measurement, U is ensemble mean velocity and U∗ and U0 are coherent and turbulent fluctuations, respectively Frequency filtering, such as LES decomposition [4], applies a homogeneous filter to identify all structures above or below a cut-off scale allowing this separation. For the reconstruction of velocity fields, it is possible to consider a reduced order representation of velocity if the number of POD modes; M is less than the total number of snapshots This is a commonly employed technique for filtering velocity field data. An iterative approach is used, increasing the cut-off and comparing the zero-crossing point of the streamwise auto-correlation from the pre-cutoff estimation and the original data When this occurs at the same location, this mode number is used. This is significantly larger than the cutoff values typically referenced elsewhere in literature
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