Viscoelastic effects on higher order statistics and on coherent structures in turbulent channel flow

In this work we study, using the results of direct numerical simulations [Housiadas and Beris, “Polymer-induced drag reduction: Viscoelastic and inertia effects of the variations in viscoelasticity and inertia,” Phys. Fluids 15, 2369 (2003)], the effects of changes in the flow viscoelasticity and the friction Reynolds number on several higher order statistics of turbulence, such as the Reynolds stress, the enstrophy, the averaged equations for the conformation tensor, as well as on the coherent structures through a Karhunen–Loeve ( K - L ) analysis and selected flow and conformation visualizations. In particular, it is shown that, as the zero friction Weissenberg number We τ 0 increases (for a constant zero friction Reynolds number Re τ 0 ) dramatic reductions take place in many terms in the averaged equations for the Reynolds stresses and in all terms of the averaged enstrophy equations. From a Karhunen–Loeve analysis of the eigenmodes of the flow we saw that the presence of viscoelasticity increases significantly the coherence and energy content of the first few modes. The K - L dimension of the flow at We τ 0 = 125 is fully one order of magnitude lower than its Newtonian counterpart. As far as the effect of viscoelasticity is concerned, it is manifested primarily by changes in the boundary layer, which are mostly accomplished by We τ 0 = 50 – 62.5 . In comparison, increasing the Re τ 0 , from 125 to 590, induces significant changes in various terms in the budgets, despite the fact that the drag reduction remains practically the same over that range. However, the near the wall region seems to change significantly only up to Re τ 0 = 395 , with few changes observed upon a further increase to Re τ 0 = 590 .