Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers

The recently discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. , Phys. Rev. Lett. vol. 121, 2018, 024502) has offered an explanation for the origin elasto-inertial turbulence that occurs at lower Weissenberg numbers ( $Wi$ ). In support this, we show using weakly nonlinear analysis subcriticality found in Page 125, 2020, 154501) is generic across neutral curve with becoming supercritical only low Reynolds $Re$ ) and high . We demonstrate can be viewed as purely elastic origin, even $Re=O(10^3)$ rather than ‘elasto-inertial’, underlying does not feed kinetic energy instability. It also introduction a realistic maximum polymer extension length, $L_{max}$ FENE-P model moves closer to inertialess $Re=0$ limit fixed ratio solvent-to-solution viscosities, $\beta$ At dilute $\beta \rightarrow 1$ $L_{max} =O(100)$ linear brought down more physically relevant $Wi\gtrsim 110$ =0.98$ compared threshold $Wi=O(10^3)$ =0.994$ reported by Khalid 127, 2021, 134502) Oldroyd-B fluid. Again, subcritical, implying nonlinearly unstable – i.e. finite-amplitude disturbances