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plane Orr-Sommerfeld problem; combination of Couette flow and Poiseuille flow; infinite dimensional matrix eigenvalue problem; inclusion of eigenvalues using a genralization of Gerschgorin's method
In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method.
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[6] Potter M. C.: Stability of plane Couette-Poiseuille flow. J. Fluid Mech. 24 (1966), 609-619. DOI 10.1017/S0022112066000855
[7] Reynolds W. C., Potter M. C.: Finite-amplitude instability of parallel shear flows. J. Fluid Mech. 27 (1967), 465-492. DOI 10.1017/S0022112067000485 | Zbl 0166.46102
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