Finite amplitude instability of plane Couette flow
- 5 December 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 83 (3) , 401-413
- https://doi.org/10.1017/s0022112077001268
Abstract
The Orr–Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the generalized Rayleigh quotient iteration. Accurate results for large values of the parameters are obtained, and these further verify the belief that plane Couette flow is stable to infinitesimal disturbances. For finite disturbances, a formal expansion based on the method of Stuart and Watson as modified by Reynolds & Potter is used. This method shows a transition to instability for a large enough amplitude.Keywords
This publication has 8 references indexed in Scilit:
- On the stability of plane Couette flow to infinitesimal disturbancesJournal of Fluid Mechanics, 1973
- Accurate solution of the Orr–Sommerfeld stability equationJournal of Fluid Mechanics, 1971
- Finite-amplitude stability of pipe flowJournal of Fluid Mechanics, 1971
- A matrix method for ordinary differential eigenvalue problemsJournal of Computational Physics, 1970
- On the non-linear stability of plane Couette flowJournal of Fluid Mechanics, 1970
- Finite-amplitude instability of parallel shear flowsJournal of Fluid Mechanics, 1967
- On the stability of viscous plane Couette flowJournal of Fluid Mechanics, 1963
- On the behaviour of small disturbances in plane Couette flowJournal of Fluid Mechanics, 1962