Physics

Reynolds number

Instability

Mechanics

Laminar flow

Inertia

Shear flow

Inertial frame of reference

Hagen–Poiseuille equation

Turbulence

Viscoelasticity

Elastic instability

Flow (mathematics)

Drag

Classical mechanics

Thermodynamics

Physical Review Letters

Viscoelastic plane Poiseuille flow is shown to become linearly unstable in the absence of inertia, in the limit of high elasticities, for ultradilute polymer solutions. While inertialess elastic instabilities have been predicted for curvilinear shear flows, this is the first ever report of a purely elastic linear instability in a rectilinear shear flow. The novel instability continues up to a Reynolds number (Re) of $O(1000)$, corresponding to the recently identified elasto-inertial turbulent state believed to underlie the maximum-drag-reduced regime. Thus, for highly elastic ultradilute polymer solutions, a single linearly unstable modal branch may underlie transition to elastic turbulence at zero Re and to elasto-inertial turbulence at moderate Re, implying the existence of continuous pathways connecting the turbulent states to each other and to the laminar base state.

Continuous Pathway between the Elasto-Inertial and Elastic Turbulent States in Viscoelastic Channel Flow