Eigenvalues of the OrrSommerfeld equation in an unbounded domain
Abstract
It is shown that, for a fourth order Hilbert space, the generalized OrrSommerfeld equation will have a finite number of eigenvalues when the mean flow exponentially approaches a constant. Several properties of and bounds for eigenvalues useful for estimating the critical Reynolds number and for numerical generation for eigenvalues are presented. It is demonstrated that a sufficiently small Reynolds number indicates that the corresponding operator is spectral.
 Publication:

Archive for Rational Mechanics and Analysis
 Pub Date:
 September 1983
 DOI:
 10.1007/BF00251509
 Bibcode:
 1983ArRMA..83..221M
 Keywords:

 Eigenvalues;
 Flow Theory;
 OrrSommerfeld Equations;
 Blasius Flow;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer