Local flow topology of a polymer-laden turbulent boundary layer

Abstract

Fine-scale flow motions are measured in a Newtonian and polymer drag-reduced turbulent boundary layer (TBL) at a common momentum thickness Reynolds number $Re_{\theta }$ of 2300. Relative to the Newtonian TBL, the polymer-laden flow has a 33 % lower skin-friction coefficient. Three-dimensional (3-D) particle tracking velocimetry is used to measure the components of the velocity gradient tensor (VGT), rate of deformation tensor (RDT) and rate of rotation tensor (RRT). The invariants in these tensors are then used to distinguish the different types of fine-scale flow motions – a method called the $\varDelta$ -criterion. Joint probability density functions (j.p.d.f.s) of the VGT invariants, $Q$ and $R$ , for the Newtonian TBL produce the familiar tear-drop pattern, commonly seen in direct numerical simulations of Newtonian turbulence. Relative to the Newtonian TBL, the polymer-laden flow has significantly attenuated values of $R$ , implying an overall reduction in fluid stretching. The invariants in the RDT, $Q_D$ and $R_D$ , imply that straining motions of the polymeric flow are more two dimensional compared with the Newtonian flow. Moreover, j.p.d.f.s of $Q_D$ and the invariant in the RRT $Q_W$ , suggest that the flow consists of fewer biaxial extensional events and more shear-dominated flow. Few, if any, experimental investigations have measured the 3-D structure of fine-scale motions in a Newtonian and polymer drag-reduced TBL using the $\varDelta$ -criterion. We provide the first experimental evidence that supports the notion that an attenuation of fluid stretching, particularly biaxial straining motions, is central to the mechanism of polymer drag reduction.