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Recent studies of pressure-driven flows of dilute polymer solutions instraight channels demonstrated the existence of two-dimensional coherentstructures that are disconnected from the laminar state and appear through asub-critical bifurcation from infinity. These travelling-wave solutions weresuggested to organise the phase-space dynamics of purely elastic andelasto-inertial chaotic channel flows. Here, we consider a wide range ofparameters, covering the purely-elastic and elasto-inertial cases, anddemonstrate that the two-dimensional travelling-wave solutions are unstablewhen embedded in sufficiently wide three-dimensional domains. Our workdemonstrates that studies of purely elastic and elasto-inertial turbulence instraight channels require three-dimensional simulations, and no reliableconclusions can be drawn from studying strictly two-dimensional channel flows.

Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows