June 2nd (Thu)

Place 名古屋大学ベンチャー・ビジネス・ラボラトリー 4F セミナー室
contact Center for Computational Science

Time 14:45-15:45
Tamer Zaki
Johns Hopkins University
Viscoelastic turbulent flows display intriguing differences from their Newtonian counterparts. Even familiar flow structures such as rolls, streaks and hairpin vortices have new origins and dynamics. A framework based on the evolution of vorticity and polymer torque is developed in order to explain these differences. The framework is adopted to study two canonical flow configurations: (i) roll-streak interactions in Couette flow and (ii) the evolution of a small-amplitude spanwise vortex in homogeneous shear. Each of the two problems focuses on different elements of the polymer-torque equation, and demonstrates the rich variety of behaviors that ensue depending on the fluid elasticity. Rolls can generate streaks via an inertial lift-up effect or an elastic polymer-stretch mechanism which is active even in the absence of inertia. The most interesting behavior arises when the timescales of viscous diffusion in the solvent and of polymer relaxation are commensurate, and the fluid can support the propagation of vorticity waves. The resulting streaks undergo cycles of amplification and decay — a unique feature of viscoelastic flows. The evolution of the spanwise vortex in viscoelastic shear flow defies our intuition from the Newtonian case entirely. The vortex in a Newtonian fluid is simply advected by the base flow and decays due to viscosity, all while energy and enstrophy decay. The Orr mechanism in that case requires a net tilt in the streamlines against the shear in order to observe energy amplification. The same vortex in a polymeric shear flow splits into two co-rotating and counter-propagating vortices that are stretched by the shear. In addition, a reverse-Orr mechanism is in effect, whereby perturbations with a net tilt with the shear amplify. These new findings provide a theoretical foundation for future analyses of transitional and turbulent viscoelastic shear flows.