The principle of exchange of stabilities for Couette flow

Herron, Isom H.; Ali, Halima N.

doi:10.1090/qam/1976370

Authors: Isom H. Herron and Halima N. Ali
Journal: Quart. Appl. Math. 61 (2003), 279-293
MSC: Primary 76E07
DOI: https://doi.org/10.1090/qam/1976370
MathSciNet review: MR1976370
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Abstract: The eigenvalue problem for the linear stability of Couette flow between two rotating concentric cylinders to axisymmetric disturbances is considered. It is proved that the principle of exchange of stabilities holds when the cylinders rotate in the same direction and the circulation decreases outwards. The proof is based on the notion of a positive operator which is analogous to a positive matrix. Such operators have a spectral property which implies the principle of exchange of stabilities.

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