Van der Waals-Zeeman Colloquium

Tuesday, 4 May 2010, 16:00

Instabilities in viscoelastic shear layers and their relation to elastic turbulence

Dr. Alexander Morozov
Univ. Edinburgh

Newtonian fluids are known to exhibit hydrodynamic instabilities and/or transition to turbulence at large enough Reynolds numbers. Recently, it has been discovered that flows of dilute polymers in simple geometries can also become unstable at very low Reynolds numbers. These purely elastic instabilities are not caused by inertia but instead are driven by anisotropic elastic stresses. Further increase of the flow rate results in a truly chaotic flow -- purely elastic turbulence.

In the first part of the talk, I will review available experimental results on purely elastic instabilities and, when possible, compare them against theoretical predictions. The emerging picture is that laminar flows with curved streamlines (Taylor-Couette, parallel-plate etc.) are linearly unstable, while parallel shear flows (plane Couette, pipe, channel) are linearly stable.

In the second part of the talk, I will discuss an attempt of modelling purely elastic turbulence. Recently, our understanding of the transition to Newtonian turbulence has significantly changed due to the discovery of the exact solutions of the Navier-Stokes equations and the introduction of the self-sustaining process by which Newtonian turbulence in parallel shear flows is sustained [F. Waleffe, Phys. Fluids, v.9, 883 (1997)]. In this mechanism, a small number of coherent structures (streamwise vortices, streaks and 3D vortices) are able to sustain themselves via a series of non-linear interactions and instabilities. This theory, dubbed the self-sustaining process, has been very successful in describing the main features of weakly turbulent states close to the transition threshold.

In this talk I will review the modern developments in Newtonian turbulence and attempt to construct a generalisation of this theory to viscoelastic flows. I will discuss how various parts of the self-sustaining process are affected by the presence of polymers and its relevance to drag reduction and purely elastic turbulence.