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A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer
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In this paper, a numerical study of the temporal eigenvalue spectrum of the Orr-Sommerfeld equation for the Blasius boundary layer is presented, where the eigenvalues located by tracing out the contour lines in the complex wave velocity plane on which the real and imaginary parts of the spectrum are zero.Abstract:
A numerical study is made of the temporal eigenvalue spectrum of the Orr-Sommerfeld equation for the Blasius boundary layer. Unlike channel flows, there is no mathematical proof that this flow has an infinite spectrum of discrete eigenvalues. The Orr-Sommerfeld equation is integrated numerically, and the eigenvalues located by tracing out the contour lines in the complex wave velocity plane on which the real and imaginary parts of the secular determinant are zero. The spectrum of plane Poiseuille flow is used as a guide to study the spectrum of an artificial two-wall flow which consists of two Blasius boundary layers. As the upper boundary of this flow moves to infinity, it is found that the portion of the spectrum with an infinite number of eigenvalues moves towards phase velocity equal to unity and the spacing between eigenvalues goes to zero. The original few eigenvalues found are the only discrete eigenvalues that exist for Blasius flow.read more
Citations
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References
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Journal ArticleDOI
Accurate solution of the Orr–Sommerfeld stability equation
TL;DR: In this article, the Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm.
Journal ArticleDOI
A completeness theorem for non-selfadjoint eigenvalue problems in hydrodynamic stability
R. C. Di Prima,G. J. Habetler +1 more
Journal ArticleDOI
The stability of steady and time-dependent plane Poiseuille flow
Chester E. Grosch,Harold Salwen +1 more
TL;DR: In this paper, the linear stability of plane Poiseuille flow has been studied both for the steady flow and also for the case of a pressure gradient that is periodic in time.