# Follow the curvature of viscoelastic stress: Insights into the steady arrowhead structure

## TL;DR

This paper investigates the steady arrowhead structure in dilute polymer solutions, revealing how flow structures and polymer stress sheets interact, and introduces a novel stressline-based formulation to interpret stress variations and pressure jumps.

## Contribution

It presents a new formulation using stresslines to better understand the relation between stress curvature and flow topology in viscoelastic flows.

## Key findings

- Stresslines relate stress variation to flow topology.
- Pressure jumps are explained by stressline curvature.
- Flow structures influence polymer stress distribution.

## Abstract

Focusing on simulated dilute polymer solutions, this letter investigates the interactions between flow structures and organized polymer stress sheets for the steady arrowhead coherent structure in a two-dimensional periodic channel flow. Formulating the problem in a frame of reference moving with the arrowhead velocity, streamlines, which are also pathlines in this frame, enables the identification of two distinct topological regions linked to two stagnation points. The streamlines help connecting the spatial distribution of polymer stress within the sheets and the dynamics of polymers transported by the flow. Using stresslines, lines parallel to the eigenvectors of polymer stress, a novel formulation of the viscoelastic stress term in the momentum transport equation proposes a more intuitive interpretation of the relation between the curvature of the stresslines, and the variation of stress along these lines, with the local flow topology. An approximation of this formulation is shown to explain the pressure jump observed in the arrowhead structure as a function of the local curvature of the polymer stress sheet.