Drag enhancement and drag reduction in viscoelastic flow

Creeping flow of polymeric fluid without inertia exhibits elastic instabilities and elastic turbulence accompanied by drag enhancement due to elastic stress produced by flow-stretched polymers. However, in inertia-dominated flow at high $\mbox{Re}$ and low fluid elasticity $El$, a reduction in turbulent frictional drag is caused by an intricate competition between inertial and elastic stresses. Here, we explore the effect of inertia on the stability of viscoelastic flow in a broad range of control parameters $El$ and $(\mbox{Re}, \mbox{Wi})$. We present the stability diagram of observed flow regimes in $\mbox{Wi}-\mbox{Re}$ coordinates and find that instabilities' onsets show unexpectedly non-monotonic dependence on $El$. Further, three distinct regions in the diagram are identified based on $El$. Strikingly, for high elasticity fluids we discover a complete relaminarization of flow at Reynolds number of the order of unity, different from a well-known turbulent drag reduction. These counterintuitive effects may be explained by a finite polymer extensibility and a suppression of vorticity at high $\mbox{Wi}$. Our results call for further theoretical and numerical development to uncover the role of inertial effect on elastic turbulence in a viscoelastic flow.