Revisiting two-dimensional viscoelastic Kolmogorov flow: a centre-mode-driven transition
Year: 2025
Type: article
Abstract: We revisit viscoelastic Kolmogorov flow to show that the elastic linear instability of an Oldroyd-B fluid at vanishing Reynolds numbers ( $Re$ ) found by Boffetta et al. ( J. Fluid Mech. , vol. 523, 2005, pp. 161–170) is the same ‘centre-mode’ instability found at much higher $Re$ by Garg et al. ( Phys. Rev. Lett. , vol. 121, 2018, 024502) in a pipe and by Khalid et al. ( J. Fluid Mech. , vol. 915, 2021, A43) in a channel. In contrast to these wall-bounded flows, the centre-mode instability exists even when the solvent viscosity vanishes (e.g. it exists in the upper-convective Maxwell limit with $Re=0$ ). Floquet analysis reveals that the preferred centre-mode instability almost always has a wavelength twice that of the forcing. All elastic instabilities give rise to familiar ‘arrowheads’ (Page et al., Phys. Rev. Lett. , vol. 125, 2020, 154501) which in sufficiently large domains and at sufficient Weissenberg number ( $W$ ) interact chaotically in two dimensions to give elastic turbulence via a bursting scenario. Finally, it is found that the $k^{-4}$ scaling of the kinetic energy spectrum seen in this two-dimensional elastic turbulence is already contained within the component arrowhead structures.
Source: Journal of Fluid Mechanics
DOI: 10.1017/jfm.2025.119
Authors: Theo Lewy, Rich R. Kerswell
Institution: University of Cambridge
Language: English
Subfield: Fluid Flow and Transfer Processes
Field: Chemical Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4408534914