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On the streaky instability of shear-thinning flow in an axially corrugated pipe
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DOI：10.1017/jfm.2026.11770.png)
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Abstract
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Shear-thinning fluids flowing near rough or wavy walls are common in engineering and biological applications; yet their behaviour remains poorly understood. Direct numerical simulation of highly shear-thinning flows is computationally demanding or even infeasible; so convenient methods for accessing this regime are highly sought after. We partially overcome this challenge for the stability analysis of the laminar base flow in the classical test case of flow in an axisymmetric corrugated pipe by employing a large-Reynolds-number asymptotic analysis. First; we obtain the analytic neutral curve for power-law fluids using only the leading order terms. To improve predictive accuracy and to handle more general Carreau–Yasuda fluids; we then develop an asymptotic preserving reduction (APR) that retains several higher order terms. Both approaches show good agreement with full system results computed using a spectral element solver for moderately shear-thinning fluids; including the streaky characteristics of the perturbation flow fields. Furthermore; we extend the stability predictions to strongly shear-thinning fluids. Using APR with Carreau–Yasuda parameters relevant to the experiments; we find that under certain conditions; the instability can arise even for very small wall undulations.
Keywords:
shear-flow instability
critical layers
complex fluids
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