(325c) Dynamic K-L Analysis of Turbulent Channel Flows

The turbulent dynamics corresponding to long-time Direct Numerical Simulation (DNS) data of Newtonian and 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 carrying 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 to conduct a comparative study of the overall flow dynamics of Newtonian and viscoelastic turbulence over long times. Time correlation analysis between pairs of K-L coefficients showed the existence of long time correlations in both Newtonian and viscoelastic turbulent results with the times further increased in the latter. These correlations have distinct pulse behavior characteristic of intermittence and quasi-periodicity in turbulence. They are used here to establish relations between the various K-L modes. In addition, phase plots of the K-L coefficients and the calculation of Liapunov exponents are employed as a mean to further characterize the large scales structures and their modifications due to the presence of viscoelasticity.

Reference *Handler RA, Housiadas KD, Beris AN, Karhunen-Loeve representations of turbulent channel flows using the method of snapshots, Int. J. Num. Meth. Fluids 52 (12): 1339-1360 (2006).