Purely elastic instabilities in shear layers

Alexander Morozov

School of Physics & Astronomy

The University of Edinburgh

James Clerk Maxwell Building

Peter Guthrie Tait Road

Edinburgh EH9 3FD

Newtonian shear layers - one-dimensional velocity profiles with a velocity jump across an imaginary interface - are known to exhibit the Kelvin-Helmholtz instability, which plays a crucial role in sustaining Newtonian turbulence in parallel shear flows close to the onset. Addition of small amounts of polymer was previously shown to inhibit the Newtonian Kelvin-Helmholtz instability and was demonstrated to be one of the mechanisms by which Newtonian coherent structures are suppressed at finite elasticity numbers.

In this talk I demonstrate that there exists a purely elastic instability of viscoelastic shear layers when the Reynolds number is small or even zero. First, I present the results of a linear stability analysis of the Oldroyd-B model and show that viscoelastic shear layers become linearly unstable when normal stresses exceed a critical value. I complement these observations by time-dependent numerical simulations and discuss a possible instability mechanism. Next, I show that this mechanism is at play in the recently observed instabilities of oscillatory shear flows of worm-like micellar solutions (see the talk by Prof Jordi Ortin in this seminar series). Time permitting, I will discuss the consequence of the shear layer instabilities for purely elastic turbulence in parallel shear flows.

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