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