On the stability of laminar flows between plates

2019/08/17 by Almog, Yaniv, Helffer, Bernard · 2 citations
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1908.06328

Abstract

Consider a two-dimensional laminar flow between two plates, so that (x₁,x₂)∈ \mathbb R ×[-1,1], given by \mathbf v(x₁,x₂)=(U(x₂),0), where U∈ C⁴([-1,1]) satisfies U^′≠0 in [-1,1]. We prove that the flow is linearly stable in the large Reynolds number limit, in two different cases: \bullet sup_x∈[-1,1] |U"(x)| + sup_x∈[-1,1] |U"(x)| ≪ min_x∈[-1,1]|U^′(x)| (nearly Couette flows), \bullet U^′′≠0 in [-1,1]. We assume either no-slip or fixed traction force conditions on the plates, and an arbitrary large (but much smaller than the Reynolds number) period in the x₁ direction.

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