Transient dynamics of turbulence growth and bursting: Effects of drag-reducing polymers

Abstract

The transient process of turbulence development and vortex breakdown from a marginal flow state dominated by streaky velocity patterns is not only essential for understanding the bypass transition into turbulence, but – in the context of viscoelastic fluids – also offers unique insight into the dynamics at high-extent and maximum drag reduction (HDR and MDR). Shooting trajectories connecting the edge state and following its unstable manifold to the turbulent basin are generated. In Newtonian flow, the growth of turbulence starts with the intensification of velocity streaks and a sharp rise in the Reynolds shear stress. It is followed by a quick breakdown into high-intensity small-scale fluctuations before entering the basin of statistical turbulence. Adding drag-reducing polymers does not affect the initial growth of turbulence but stabilizes the primary streak-vortex structure. As a result, the vortex breakdown stage is circumvented. Polymer deformation is insignificant until the vortex breakdown, after which polymer stress rapidly shoots up. At high Weissenberg number Wi, loss of turbulent kinetic energy through polymer elastic conversion is comparable to viscous dissipation. Beyond bypass transition, the transient process studied here closely resembles the bursting phase of the self-sustaining cycle of turbulence. Our results indicate that at high Wi (i.e., HDR) polymer effects can significantly reduce bursting by rerouting the trajectory of turbulent dynamics.