Purely Elastic Turbulence and Exact Coherent Structures

Turbulence, the seemingly random motion of fluid at high flow rates, is commonplace and yet poorly understood. From the mixing of milk in tea, billowing smoke and the roiling motion of boiling water, turbulence is everywhere. However, we still are unable to predict when the transition to this seemingly disordered motion will occur for a given flow rate, viscosity and geometry. 'Exact coherent structures' (a specific kind of long lifetime patterns in the flow) are a new approach that give more accurate predictions of the transition to and behaviour of a turbulent flow. Purely elastic turbulence is a new kind of turbulence due to the elasticity instead of the inertia of a viscoelastic fluid. This kind of turbulence is thought to commonly occur in flows of polymer and biopolymer solutions as well as controlling the rate of production of many plastic products.

I will present some results obtained during the first attempt to find these exact coherent structures in flows of viscoelastic fluids. First I will give an introduction to the idea of a self-sustaining process for Newtonian fluids, found by F. Waleffe in 1997. Then I will explain the analogous self-sustaining process in viscoelastic plane Couette flow and discuss how it might lead to an exact coherent structure.

F. Waleffe. On a self-sustaining process in shear flows. Phys. Fluids 9: 883-900, 1997.

R. G. Larson. Turbulence without inertia. Nature 405: 27-28, 2000.