Tables of Eigenvalues and Eigenfunctions of the Orr-Sommerfeld Equation for Plane Poiseuille Flows.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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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 nmy, n 1,2,3,4 m 1,2,...8 are presented in tabular and graphical form. In addition the function, chi sub nmy, which is orthogonal to phi sub nmy, over the interval -1 or - y or - plus or minus 1 is tabulated. In a previous report Gawain and Clark1971 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
- Theoretical Mathematics
- Fluid Mechanics