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arXiv · 2108.03126

Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

Martin Lellep·Moritz Linkmann·Bruno Eckhardt·Alexander Morozov
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Abstract

We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

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Martin Lellep, Moritz Linkmann, Bruno Eckhardt, Alexander Morozov. 2021-09-21. Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions. https://doi.org/10.1017/jfm.2021.840

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