Weissenberg Number Dependence of Linear Mechanisms in Polymer Drag-Reduced Turbulent Channel Flow*

It is well-known that small amounts of high-molecular weight polymers can drastically reduce turbulent drag in a liquid. Furthermore, recent work has shown that studying polymers in turbulence can shed light on the nature of the self-sustaining mechanisms of wall turbulence. This work analyzes the linear mechanisms present in polymer drag-reduced turbulence, with an emphasis on how these mechanisms change with the level of drag reduction. In particular, we extend resolvent analysis to the study of viscoelastic turbulence in order to identify the most amplified velocity and conformation tensor modes at Weissenberg numbers representative of low drag reduction and the recently discovered elastoinertial turbulence. The results predicted by the resolvent analysis are in good qualitative agreement with observations from direct numerical simulations and complement existing work for laminar viscoelastic flows. Furthermore, they provide a starting point for efficient low-order models of viscoelastic turbulence.