Orr-Sommerfeld equation and complex deformation
Abstract
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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