Narwhals and their blessings: exact coherent structures of elastic turbulence in channel flows

Abstract: Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behaviour. When subjected to external flows, dilute polymer solutions develop elastic turbulence - a unique chaotic flow state absent in Newtonian fluids such as water. Unlike turbulence in Newtonian fluids, elastic turbulence arises from polymer stretching and alignment in the flow, and can occur even at vanishing inertia. While experimental realisations of elastic turbulence are well documented, its underlying mechanism remains poorly understood. In this paper, we present a perspective on the transition to elastic turbulence in pressure-driven channel flows, drawing on recent computational work from our group. We outline our current understanding of the transition in both two and three spatial dimensions, centred on two key building blocks: (i) narwhals, exact coherent states of the flow, and (ii) blessings, spatio-temporal intermittent states made up of several localised narwhal solutions. This contribution is based on a talk given by one of us (A.M.) at the 2024 APS DFD meeting.