The theory of stability of spatially periodic parallel flows

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Abstract
The stability of a parallel flow periodic in the direction normal to the stream is investigated theoretically. Critical Reynolds numbers are calculated for a general velocity profile including widely separated wakes. The critical mode of disturbance is found to have the same period as the basic flow. Growing modes with much larger periods exist, however, at slightly supercritical values of the Reynolds number. The analysis of various limiting cases explains the qualitative difference in the shape of the neutral curves depending on the period of the disturbance. In connection with the results obtained in this paper, the stability of non-parallel periodic flows is briefly discussed.

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