Dynamic K-L Analysis of the Coherent Structures in Turbulent Viscoelastic Channel Flows

Abstract

The turbulent dynamics corresponding to long‐time Direct Numerical Simulation (DNS) data of viscoelastic turbulent channel flows is analyzed here through a projection of the velocity fields into a set of Karhunen‐Loeve (K‐L) modes, large enough to contain, on the average, more than 90% of the fluctuating turbulence energy. Previous static K‐L analyses have demonstrated a dramatic decrease in the K‐L dimensionality (and, correspondingly, the number of modes caπying most of the turbulent energy) as viscoelasticity increases in turbulent channel flows; this is also consistent to the increasing importance of large coherent structures for viscoelastic turbulent flows, as was also revealed in previous flow visualizations of DNS data. Here we use the K‐L modes dynamically in viscoelastic turbulence to better understand the role of coherent structures and viscoelasticity. In particular, we calculate the viscoelastic conformation field developed in response to the velocity field reconstructed from selected KL representations and compare the results against the full DNS predictions. The significance of these results in building low dimensional models for viscoelastic turbulence is also going to be addressed.