On the spectrum localization of the Orr--Sommerfeld problem for large Reynolds numbers
This paper is devoted to the Orr-Sommerfeld problem and to the corresponding model problem \(-i\varepsilon^2y''-q(x)y=-\lambda y\), \(y(-1)=y (1)=0\), where small values of parameter \(\varepsilon\) correspond to large Reynolds numbers. The main result of the paper is the following: as \(\varepsilon \) tends to zero, the spectrum of Orr-Sommerfeld problemf for \(q(x)=x\) and \(q(x)= x^2\) is localized on critical curves which are the same as in the model problem. Moreover, the authors present the main terms of asymptotic formulas for eigenvalue distributions.
asymptotic formulas for eigenvalue distributions
scientific article; zbMATH DE number 1928314