Reτ scaling of POD modes in plane channel flow

Abstract

This article studies how the proper orthogonal decomposition eigenvectors and eigenvalues of the two-point velocity correlation tensor scale with Reτ in turbulent channel flows. To this effect, the two-point correlation tensor is computed from velocity fields extracted from the Direct Numerical Simulations (DNS) of plane channel flows at Reτ = 547 and Reτ = 934. The analysis reveals that the eigenvalues exhibit a high degree of scaling with Reτ, across a very wide range of streamwise and spanwise wavenumbers. The eigenvectors also show near complete independence from Reτ, as long as the wall-normal lengthscales larger than the channel height are removed. The poor Reτ scaling of turbulent structures larger than the channel height is well documented in the literature, and thus one would not expect eigenvectors corresponding to these scales to exhibit favorable Reτ scaling. Two-point velocity correlations and their eigenvectors are also computed using Large Eddy Simulations (LES) at Reτ = 1000 and compared to the results of the DNS at Reτ = 934. Both the correlations and eigenvectors matched very well between LES and DNS.