New direction and perspectives in elastic instability and turbulence in various viscoelastic flow geometries without inertia

We shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertialess flows with curved streamlines. Then we describe a theory of elastic turbulence and prediction of elastic waves Re 1 and Wi 1, which speed depends on the elastic stress similar to the Alfven waves in magneto-hydrodynamics and in a contrast to all other, which speed depends on medium elasticity. Since the established and testified mechanism of elastic instability of viscoelastic flows with curvilinear streamlines becomes ineffective at zero curvature, so parallel shear flows are proved linearly stable, similar to Newtonian parallel shear flows. However, the linear stability of parallel shear flows does not imply their global stability. Here we switch to the main subject, namely a recent development in inertialess parallel shear channel flow of polymer solutions. In such flow, we discover an elastically driven instability, elastic turbulence, elastic waves, and drag reduction down to relaminarization that contradict the linear stability prediction. In this regard, we discuss briefly normal versus non-normal bifurcations in such flows, flow resistance, velocity and pressure fluctuations, and coherent structures and spectral properties of a velocity field as a function of Wi at high elasticity number. Published under an exclusive license by AIP Publishing.

Automated summary

This article briefly describes the main results of elastically driven instabilities and elastic turbulence in viscoelastic inertialess flows with curved streamlines. It then introduces a theory of elastic turbulence and predicts elastic waves based on the elastic stress, similar to Alfven waves in magneto-hydrodynamics. In contrast to other waves, the speed of these elastic waves depends on the medium's elasticity. The linear stability of parallel shear flows is discussed, along with recent developments in the parallel shear channel flow of polymer solutions. Elastically driven instabilities, elastic turbulence, elastic waves, and drag reduction are observed in this flow, contradicting linear stability predictions. The resistance of the flow, velocity and pressure fluctuations, coherent structures, and spectral properties of the velocity field are also briefly discussed as functions of the elasticity number.