Tollmien-Schlichting route to elastoinertial turbulence in channel flow

TL;DR

This paper investigates the transition from Tollmien-Schlichting waves to elastoinertial turbulence in viscoelastic channel flow, revealing how flow structures evolve with parameters and identifying a coil-stretch transition linked to turbulence onset.

Contribution

It characterizes the evolution of TS attractors in viscoelastic flow and connects flow structure changes to the onset of elastoinertial turbulence, highlighting a coil-stretch transition mechanism.

Findings

TS attractors evolve with Reynolds and Weissenberg numbers

Flow transitions from localized polymer stretch to layered sheets

Identification of coil-stretch transition at critical flow conditions

Abstract

Direct simulations of two-dimensional channel flow of a viscoelastic fluid have revealed the existence of a family of Tollmien-Schlichting (TS) attractors that is nonlinearly self-sustained by viscoelasticity [Shekar et al., J.Fluid Mech. 893, A3 (2020)]. Here, we describe the evolution of this branch in parameter space and its connections to the Newtonian TS attractor and to elastoinertial turbulence (EIT). At Reynolds number $Re=3000$, there is a solution branch with TS-wave structure but which is not connected to the Newtonian solution branch. At fixed Weissenberg number, $Wi$ and increasing Reynolds number from 3000-10000, this attractor goes from displaying a striation of weak polymer stretch localized at the critical layer to an extended sheet of very large polymer stretch. We show that this transition is directly tied to the strength of the TS critical layer fluctuations and can be attributed to a coil-stretch transition when the local Weissenberg number at the hyperbolic stagnation point of the Kelvin cat's eye structure of the TS wave exceeds $\frac{1}{2}$. At $Re=10000$, unlike $3000$, the Newtonian TS attractor evolves continuously into the EIT state as $Wi$ is increased from zero to about $13$. We describe how the structure of the flow and stress fields changes, highlighting in particular a "sheet-shedding" process by which the individual sheets associated with the critical layer structure break up to form the layered multisheet structure characteristic of EIT.