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

Abstract

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. {\em J. Fluid Mech.} {\bf 915}, A43, 2021) are substantially subcritical reaching much lower Weissenberg ($Wi$) numbers than on the neutral curve at a given Reynolds ($Re$) number over $Re\in [0,3000]$. The travelling waves on the lower branch are surprisingly weak indicating that viscolastic 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, $\approx 37$ at $Re=3000$ down to $\approx 7.5$ 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 $Wi\lesssim 50$ for higher polymer concentrations - $\beta \in [0.5,0.97)$ -- 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. {\em arXiv}.2006.06770 (2020) - 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.

arXiv comment21 pages, 12 figures

References in corpus (24)

• Elastic turbulence in a polymer solution flow
• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• Efficient Mixing at low Reynolds numbers using polymer additives
• Elasto-inertial turbulence
• A nonlinear elastic instability in channel flows at low Reynolds numbers
• On the mechanism of elasto-inertial turbulence
• Transition in pipe flow: the saddle structure on the boundary of turbulence
• Laminar-turbulent boundary in plane Couette flow
• Viscoelastic pipe flow is linearly unstable
• Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction
• Understanding viscoelastic flow instabilities: Oldroyd-B and beyond
• The center-mode instability of viscoelastic plane Poiseuille flow
• Critical-layer structures and mechanisms in elastoinertial turbulence
• Exact travelling wave solutions in viscoelastic channel flow
• A continuous pathway between the elasto-inertial and elastic turbulent states in viscoelastic channel flow
• Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re
• Linear instability of viscoelastic pipe flow
• A first coherent structure in elasto-inertial turbulence
• Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
• Elastically driven Kelvin-Helmholtz-like instability in planar channel flow
• Self-sustained elastoinertial Tollmien-Schlichting waves
• Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia
• Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows
• Subcritical instabilities in plane Poiseuille flow of an Oldroyd-B fluid

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• Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
• Inertial enhancement of the polymer diffusive instability
• A unified view of elastic and elasto-inertial turbulence in channel flows at low and moderate Reynolds numbers
• Preserving large-scale features in simulations of elastic turbulence
• On the large-Weissenberg-number scaling laws in viscoelastic pipe flows
• Coherent structures in Newtonian and viscoelastic turbulent planar jets
• The broken link between space and time in elastic turbulence