Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number

Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of the recently discovered linear instability of viscoelastic channel flow (Khalid et al., J. Fluid Mech., vol. 915, 2021, A43) are substantially subcritical reaching much lower Weissenberg (Wi) numbers than on the neutral curve at a given Reynolds (Re) number over Re is an element of [0, 3000]. The travelling waves on the lower branch are surprisingly weak indicating that viscoelastic channel flow is susceptible to (nonlinear) instability triggered by small finite-amplitude disturbances for Wi and Re well below the neutral curve. The critical Wi for these waves to appear in a saddle node bifurcation decreases monotonically from, for example, approximate to 37 at Re = 3000 down to approximate to 7.5 at Re = 0 at the solvent-to-total-viscosity ratio beta = 0.9. In this latter creeping flow limit, we also show that these waves exist at Wi less than or similar to 50 for higher polymer concentrations, beta is an element of [0.5, 0.97), where there is no known linear instability. Our results therefore indicate that these travelling waves, found in simulations and named 'arrowheads' by Dubief et al. (Phys. Rev. Fluids, vol. 7, 2022, 073301), exist much more generally in (Wi, Re, beta) parameter space than their spawning neutral curve and, hence, can either directly, or indirectly through their instabilities, influence the dynamics seen far away from where the flow is linearly unstable. Possible connections to elastic and elasto-inertial turbulence are discussed.