On the Stability of Periodic Solutions in Fluid Mechanics
In various stability problems of fluid mechanics, such as the Taylor problem, the Bénard problem or the problem of plane Poiseuille flow, there exists a critical value of the governing parameter R (Taylor number, Rayleigh number, Reynolds number) above which the flow becomes unstable (according to linear theory) to spatially periodic disturbances of which the wave number k lies within an interval k 1(R) < k < k 2(R). Non-linear theories have shown that spatially periodic solutions which are bounded for all time can exist in such supercritical conditions. The stability of these supercritical periodic solutions, and investigation of further possible solutions in the supercritical region, are the subject of this paper.
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