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A method of getting approximate solutions to the orr‐sommerfeld equation for flow on a vertical wall
Author(s) -
Anshus Byron E.,
Goren Simon L.
Publication year - 1966
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690120529
Subject(s) - eigenvalues and eigenvectors , simple (philosophy) , reynolds number , mathematics , flow (mathematics) , stability (learning theory) , surface (topology) , function (biology) , mathematical analysis , velocity potential , free surface , exact solutions in general relativity , mechanics , physics , geometry , turbulence , boundary value problem , computer science , philosophy , epistemology , quantum mechanics , machine learning , evolutionary biology , biology
A method is presented for getting approximate solutions to the Orr‐Sommerfeld equation for free surface flows. The method consists of replacing the velocity, normally a function of distance from the wall, by its value at the free surface while the second derivative of the velocity is kept at its true value. This permits a simple solution to the equation and the eigenvalues can then be determined by a simple and rapid numerical technique. Comparison of this approximate solution for the flow of a thin film on a vertical wall with existing exact numerical solutions and with analytical results valid only for small Reynolds numbers shows the approximation to be quite accurate for most practical values of the parameters and suggests that the method will be useful in investigating the stability of related flows.