Braided Vortices in the Taylor–Couette System: Transition to Turbulence through Tertiary and Quaternary States

Abstract

This manuscript extends the recent work on the Taylor–Couette problem in the small gap limit to include braided vortex flow (Bvf) solutions. Theoretical results are derived using the small-gap approximation and the corresponding equations are analysed numerically. This reveals that for certain values of the axial wavenumber (β), steady Bvf vortices can be realized for Reynolds numbers (R) that are prevalent at the wavy twist stability boundary. These vortices become unstable to states that are oscillatory, quasi-periodic and eventually aperiodic as R increases. This study further examines the bifurcation characteristics of Bvf from the Taylor vortices of variable wavenumbers β, thus also exploring the transition to turbulence and highlighting the role of braided vortex flows in this process. The possibility of interactions between the wavy twist and subharmonic drifting wave of [1*] is also explored. The findings provide new insights into the complex dynamics of the Taylor–Couette system, contributing to a deeper understanding of the transition from laminar flow to turbulence and are expected to stimulate further experimental investigations in this intriguing area of fluid dynamics.