Tables of eigenvalues and eigenfunctions of the Orr-Sommerfeld equation for plane Poiseuille flows

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Authors
Clark, W. H.
Gawain, Theodore Henry
Subjects
Hydrodynamic stability
finite-differences
plane Poiseuille flow.
Advisors
Date of Issue
1971-09-10
Date
9/10/1971
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
In the report the authors present a numerical technique for computing the eigenvalues and eigenfunctions of the Orr-Sommerfeld equation for infinitesimal disturbances in plane Poiseuille flows. For the case alpha = 1.0, Rsube = 6667 the eigenvalues, beta sub Nm, (n = 1,2,3,4 m = 1,2,...199) and eigenfunctions, phi sub nm(y), (n = 1,2,3,4 m = 1,2,...8) are presented in tabular and graphical form. In addition the function, chi sub nm(y), which is orthogonal to phi sub nm(y), over the interval -1 or - y or - plus or minus 1 is tabulated. In a previous report (Gawain and Clark)1971) it was shown that these eigenfunctions can be extremely useful in describing certain aspects of the nonlinear mechanics of wave disturbances in plane Poiseuille flows. It is hoped that the present report will serve both as a complement to the previously mentioned report and as a useful reference for similar future investigations. (Author)
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS-57GN71092A
Sponsors
Funder
Format
184 p. : ill. ; 28 cm.
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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