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arXiv · 2503.17451

A model for Reynolds-dependent linear instability in wall-bounded shear flows

John O. Dabiri·Anthony Leonard
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Abstract

Recent work demonstrated that alternative models to the "no-slip" boundary condition for incipient flow perturbations can produce linear instabilities that do not arise in the classical formulation. The present study introduces a Robin-type boundary condition with explicit Reynolds-number dependence, which leads to a more physically realistic transition to instability in wall-bounded shear flows. The results show that instability occurs within a Reynolds number range consistent with empirical observations. A physical interpretation of the modified boundary condition in terms of near-wall vorticity dynamics is discussed.

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John O. Dabiri, Anthony Leonard. 2025-03-21. A model for Reynolds-dependent linear instability in wall-bounded shear flows. https://arxiv.org/abs/2503.17451

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