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Purely elastic instabilities in free shear layers

Alexander Morozov, School of Physics, The University of Edinburgh, JCMB

16 November 2009

Free shear layers — 1D velocity profiles with a velocity jump across some (imaginary) interface — are known to exhibit Kelvin-Helmholtz instability which plays a crucial role in sustaining Newtonian turbulence close to the onset. Addition of small amounts of polymer was previously shown to inhibit Newtonian Kelvin-Helmholtz instability (large Reynolds number regime) and was argued by some to be a possible explanation for the drag-reduction phenomenon.

Here we show that even though polymers do inhibit Newtonian Kelvin-Helmholtz instability at large Reynolds numbers, there exists a purely elastic instability of viscoelastic shear layers when Reynolds number is small or even zero. We perform linear stability analysis of the Oldroyd-B equation and show that viscoelastic shear layers become linearly unstable when normal stresses exceed a critical value. We discuss the mechanism underlying this instability and argue that it might be connected to purely elastic instabilities in parallel shear flows of viscoelastic fluids and purely elastic turbulence.

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