Onset of Taylor-Görtler instability in accelerated circular Couette flow

Abstract

The onset of Taylor-Gortler 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 Tac at which Taylor vortices set in between two concentric cylinders. For Ta > Tac Taylor-Gortler vortices are detected experimentally at a certain elapsed time. In the present study the critical time tc 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 tm ≈ 4tc. 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.