On the spectrum localization of the Orr--Sommerfeld problem for large Reynolds numbers
type: Item
instance of: scholarly article
title: On the spectrum localization of the Orr--Sommerfeld problem for large Reynolds numbers
zbMATH Open document ID: 1022.76016
DOI: 10.1023/A:1020588429647
author: A. A. Shkalikov
author: S. N. Tumanov
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 1928314
zbMATH Keywords: spectrum localization
zbMATH Keywords: large Reynolds numbers
zbMATH Keywords: small parameter
zbMATH Keywords: Orr-Sommerfeld problem
zbMATH Keywords: critical curves
zbMATH Keywords: asymptotic formulas for eigenvalue distributions
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1020588429647
OpenAlex ID: W96245290
description: scientific article; zbMATH DE number 1928314