Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions. (10th December 2021)

• Record Type: Journal Article
• Authors: Lellep, Martin; Linkmann, Moritz; Eckhardt, Bruno; Morozov, Alexander
• Is Part Of: Journal of fluid mechanics. Volume 928(2021)
• Publication Date: 2021-12-10
• Subjects: polymers -- viscoelasticity -- shear-flow instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.840
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.