A NUMERICAL TREATMENT OF THE ORRSOMMERFELD EQUATION IN THE CASE OF A LAMINAR JET

1 January 1960

journal article
Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics

Vol. 13 (3) , 300-313
https://doi.org/10.1093/qjmam/13.3.300

Abstract

A numerical method is described for determining points on the neutral stability curve of a laminar jet. This involves the numerical solution of the Orr-Sommerfeld equation, given by with ω = sech²y and the boundary conditions The method used is to expand ø in a series of Chebyshev polynomials whose argument is the transformed independent variable t = tanh y, and solve the recurrence relations which exist between the coefficients in the expansion. An iterative technique is used for determining the parameters R and re c so that, for given α and zero im c.a non-trivial solution ø exists. A few points on the resulting curve of R against a, the ‘neutral stability curve’, are found in order to estimate the ‘critical Reynolds number’, R_c, which is the minimum value of R for which such a solution exists.

Keywords

This publication has 0 references indexed in Scilit: