A reverse transition route from inertial to elasticity-dominated turbulence in viscoelastic Taylor–Couette flow

Abstract

A high-order transition route from inertial to elasticity-dominated turbulence (EDT) in Taylor–Couette flows of polymeric solutions has been discovered via direct numerical simulations. This novel two-step transition route is realized by enhancing the extensional viscosity and hoop stresses of the polymeric solution via increasing the maximum chain extension at a fixed polymer concentration. Specifically, in the first step inertial turbulence is stabilized to a laminar flow much like the modulated wavy vortex flow. The second step destabilizes this laminar flow state to EDT, i.e. a spatially smooth and temporally random flow with a $-3.5$ scaling law of the energy spectrum reminiscent of elastic turbulence. The flow states involved are distinctly different to those observed in the reverse transition route from inertial turbulence via a relaminarization of the flow to elasto-inertial turbulence in parallel shear flows, underscoring the importance of polymer-induced hoop stresses in realizing EDT that are absent in parallel shear flows.