Revisiting elastic turbulence in Kolmogorov flow: the centre-mode causes transition

Viscoelastic Kolmogorov flow is known to undergo an elastic linear instability at vanishing Reynolds numbers (Boffetta et al. 2005). We revisit this to confirm that the inertialess dynamics are entirely due to the centre-mode instability of Garg et al. 2018 in a pipe and Khalid et al. 2021 in a channel. The instability persists even when the solvent viscosity vanishes (i.e. in the Upper Convective Maxwell limit), and Floquet analysis shows that the preferred mode typically has a wavelength twice that of the forcing. It is also found that for a given streamwise domain size, the instability always disappears for sufficiently large Weissenberg number (W). The centre mode instability gives rise to familiar `arrowheads' (Page et al. 2020) which at sufficient W interact chaotically in 2D to give elastic turbulence.