Taylor-Couette flow in the narrow-gap limit

A Cartesian representation of the Taylor-Couette system in the vanishing limit of the gap between coaxial cylinders is presented, where the ratio, mu , of the angular velocities, omega(i) and omega(o) , of the inner and the outer cylinders, respectively, affects its axisymmetric flow structures. Our numerical stability study finds remarkable agreement with previous studies for the critical Taylor number, T-c(mu), for the onset of axisymmetric instability. The Taylor number T can be expressed as T = omega (R - omega ), where omega (the rotation number) and .R (the Reynolds number) in the Cartesian system are related to the average and the difference of omega(i) and omega(o). The instability sets in the region (omega , R) -> (0, infinity), while the product of omega and R is kept finite. Furthermore, we developed a numerical code to calculate nonlinear axisymmetric flows. It is found that the mean flow distortion of the axisymmetric flow is antisymmetric across the gap when mu =1, while a symmetric part of the mean flow distortion appears additionally when mu &NOTEQUexpressionL;1. Our analysis also shows that for a finite .R all flows with mu &NOTEQUexpressionL; 1 approach the .R axis, so that the plane Couette flow system is recovered in the vanishing gap limit.This article is part of the theme issue Taylor- Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Automated summary

A Cartesian representation of the Taylor-Couette system in the vanishing limit of the gap between cylinders is presented, showing the influence of the angular velocities ratio on the axisymmetric flow structures. Numerical stability study confirms previous findings on the critical Taylor number for the onset of axisymmetric instability. Additionally, the mean flow distortion of the axisymmetric flow exhibits symmetric or antisymmetric distribution across the gap depending on the value of the angular velocities ratio.