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arXiv · 2211.09063

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

Martin Lellep·Moritz Linkmann·Alexander Morozov
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Abstract

Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely-elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.

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Martin Lellep, Moritz Linkmann, Alexander Morozov. 2022-11-16. Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows. https://doi.org/10.1017/jfm.2023.100

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