The energetic motions in turbulent pipe flow

Snapshot and classical proper orthogonal decomposition (POD) are used to examine the large-scale, energetic motions in fully developed turbulent pipe flow at ReD = 47,000 and 93,000. The snapshot POD modes come in pairs, representing the same azimuthal mode number but with a simple phase shift. The first 10 snapshot POD modes, associated with the very large scale motions (VLSMs), contribute 43% of the average Reynolds shear stress, and for first 80 modes u' and v' are anti-correlated so that they all contribute to positive shear stress events. The attached motions are contained in the lower order modes, and detached motions do not appear until snapshot POD mode numbers ?15. We find that snapshot POD can introduce mode mixing, which is avoided in classical POD. Classical POD also gives frequency information, confirming that the low order modes capture well the behavior of the very large scale motions.