Summary
The onset of Taylor-Görtler vortices in a developing Couette flow induced by the inner cylinder rotating with time-dependent manner is analyzed using linear theory. It is well known that there is a critical Taylor number Ta c at which Taylor vortices set in between two concentric cylinders. For Ta > Ta c Taylor-Görtler vortices are detected experimentally at a certain elapsed time. In the present study the critical time t c to represent the onset of a fastest growing instability, which then grows as toroidal vortices, is analyzed using the propagation theory. Available experimental data indicate that for large Ta secondary motion is detected starting from a certain time t m ≈ 4t c. This means that the growth period of initiated instabilities is needed for secondary motion to be detected experimentally. The new measures to represent the onset of a fastest growing instability in the primary time-dependent Couette flow are suggested.
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Kim, M.C., Choi, C.K. Onset of Taylor-Görtler instability in accelerated circular Couette flow. Acta Mechanica 188, 79–92 (2007). https://doi.org/10.1007/s00707-006-0378-8
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DOI: https://doi.org/10.1007/s00707-006-0378-8