Three-dimensional elastic turbulence in Taylor–Couette flows of dilute polymer solutions has been realized and thoroughly investigated via direct numerical simulations. A novel flow transition pathway from elastically dominated turbulence to solitary vortex pairs (or diwhirls) and eventually to elastic turbulence is observed by decreasing the fluid inertia ($Re$) over seven orders of magnitude, i.e. from $Re=1000$ to $0.0001$. The dominant spatio-temporal flow features in the elastic turbulence regime are those of large-scale unsteady diwhirls and small-scale axial and azimuthal travelling waves in the outer and inner halves of the gap, respectively. Moreover, it is conclusively shown that production of turbulent kinetic energy in purely elastic turbulence solely arises due to the stochastic nature of polymer stretch/relaxation. Overall, based on this comprehensive numerical investigation, the differences in the underlying fluid physics that give rise to turbulent fluctuations in elastically dominated and purely elastic turbulence have been delineated.

Direct numerical simulation of spanwise-rotation-driven flow transitions in viscoelastic plane Couette flow from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow state followed by full relaminarization is reported for the first time. Specifically, this novel flow transition begins with a drag-reduced inertial turbulent flow state at a low rotation number $0\leqslant Ro \leqslant 0.1$, and then transitions to a rotation/polymer-additive-driven drag-enhanced inertial turbulent regime, $0.1\leqslant Ro \leqslant 0.3$. In turn, the flow transitions to a drag-enhanced elasto-inertial turbulent state, $0.3\leqslant Ro \leqslant 0.9$, and eventually relaminarizes at $Ro=1$. In addition, two novel rotation-dependent drag enhancement mechanisms are proposed and substantiated. (1) The formation of large-scale roll cells results in enhanced convective momentum transport along with significant polymer elongation and stress generated in the extensionally dominated flow between adjacent roll cells at $Ro\leqslant 0.2$. (2) Coriolis-force-generated turbulent vortices cause strong incoherent transport and homogenization of significant polymer stress in the bulk via their vortical circulations at $Ro=0.5 - 0.9$.

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.

The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ($Re$) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

Direct numerical simulation of polymer-induced flow relaminarization of turbulent spanwise-rotating plane Couette flow (RPCF) is reported for the first time. Specifically, the reverse transition pathway from a Newtonian turbulent RPCF to a fully relaminarized drag enhanced viscoelastic flow has been elucidated. Evidently, this transition occurs gradually by weakening and eventual elimination of small-scale vortices as the Weissenberg number ($Wi$) is enhanced, paving the way for a two-dimensional laminar flow consisting of large-scale and highly organized roll cells. The influence of polymer additives on convective momentum exchange by large-scale roll cells and small-scale turbulent vortices, namely, the drag reduction (DR) realized by elimination of turbulent vortices and the significant drag enhancement (DE) that results from polymer roll cell interactions has been identified as the mechanism of DE. The observed vortical changes point to a universal mechanism for the coupling of polymer chains and turbulent vortices in wall-bounded viscoelastic DE and DR flows.

We report direct numerical simulation results that clearly elucidate the mechanism that leads to curvature dependence of drag enhancement (DE) in viscoelastic turbulent Taylor–Couette flow. Change in the angular momentum transport and its inherent link to transitions in vortical flow structures have been explored to depict the influence of the curvature of the flow geometry on DE. Specifically, it has been demonstrated that a transition in vortical structures with increasing radius ratio leads to weakening and elimination of the small-scale Görtler vortices and development and better organization (occupying the entire gap) of large-scale Taylor vortices as also evinced by the patterns of angular momentum current. The commensurate change in DE and its underlying mechanism are examined by contributions of convective flux and polymeric stress to the angular momentum current. The present finding paves the way for capturing highly localized elastic turbulence structures in direct numerical simulation by increasing geometry curvature in traditional turbulent curvilinear flows.