Orr-Sommerfeld equation and complex deformation
arXiv:2503.22274
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.
v2: Added a formula for the first order perturbation in the case of a simple resonance. Some typos fixed