English

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

Fluid Dynamics 2022-06-22 v2 Classical Physics

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.

Keywords

Cite

@article{arxiv.2108.03126,
  title  = {Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions},
  author = {Martin Lellep and Moritz Linkmann and Bruno Eckhardt and Alexander Morozov},
  journal= {arXiv preprint arXiv:2108.03126},
  year   = {2022}
}

Comments

10 pages, 7 figures