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Orr-Sommerfeld equation and complex deformation

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arxiv 2503.22274 v2 pith:EJXZHCMV submitted 2025-03-28 math.AP

Malo Jézéquel , Jian Wang This is my paper · ORCID
classification math.AP
keywords equationcomplexdeformationrayleighresonancesshearanalyticityassumption
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For shear flows in a 2D channel, we define resonances near regular values of the shear profile for the Rayleigh equation under an analyticity assumption. This is done via complex deformation of the interval on which Rayleigh equation is considered. We show such resonances are inviscid limits of the eigenvalues of the corresponding Orr--Sommerfeld equation.

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  1. Stability of laminar monotone shear flows in a channel for high Reynolds number

    math.AP 2025-07 conditional novelty 6.0 of 10

    Monotone shear flows in a channel are linearly stable at high Reynolds number for all perturbation wavelengths, including long waves, if a Schrödinger-type operator is strictly positive at all inflection points.

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