Accurate solution of the Orr–Sommerfeld stability equation
- 29 November 1971
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 50 (4) , 689-703
- https://doi.org/10.1017/s0022112071002842
Abstract
The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm. It is shown that results of great accuracy are obtained very economically. The method is applied to the stability of plane Poiseuille flow; it is found that the critical Reynolds number is 5772·22. It is explained why expansions in Chebyshev polynomials are better suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.This publication has 10 references indexed in Scilit:
- The fast Fourier transform algorithm: Programming considerations in the calculation of sine, cosine and Laplace transformsJournal of Sound and Vibration, 1970
- A matrix method for ordinary differential eigenvalue problemsJournal of Computational Physics, 1970
- The stability of steady and time-dependent plane Poiseuille flowJournal of Fluid Mechanics, 1968
- Chebyshev Collocation Methods for Ordinary Differential EquationsThe Computer Journal, 1964
- On the behaviour of small disturbances in plane Couette flowJournal of Fluid Mechanics, 1962
- Numerical Methods for Scientists and Engineers.Journal of the Royal Statistical Society. Series A (General), 1962
- Chebyshev Methods for Ordinary Differential EquationsThe Computer Journal, 1962
- On the application of infinite systems of ordinary differential equations to perturbations of plane Poiseuille flowQuarterly of Applied Mathematics, 1958
- Calculated Amplified Oscillations in the Plane Poiseuille and Blasius FlowsJournal of the Aeronautical Sciences, 1954
- The Stability of Plane Poiseuille FlowPhysical Review B, 1953