Routes to turbulence in Taylor-Couette flow

TL;DR

This paper reviews two distinct pathways to turbulence in Taylor-Couette flow, highlighting the roles of flow symmetry, bifurcation theory, and the rotation number in the transition process.

Contribution

It provides a comparative analysis of the linear instability route and the abrupt transition route to turbulence, integrating bifurcation theory and statistical approaches.

Findings

Inner-cylinder dominated flows show sequential loss of symmetry.

Outer-cylinder dominated flows transition abruptly to turbulence.

Rotation number influences the existence of laminar-turbulent patterns.

Abstract

Fluid flows between rotating concentric cylinders exhibit two distinct routes to turbulence. In flows dominated by inner-cylinder rotation, a sequence of linear instabilities leads to temporally chaotic dynamics as the rotation speed is increased. The resulting flow patterns occupy the whole system and sequentially lose spatial symmetry and coherence in the transition process. In flows dominated by outer-cylinder rotation, the transition is abrupt and leads directly to turbulent flow regions that compete with laminar ones. We here review the main features of these two routes to turbulence. Bifurcation theory rationalises the origin of temporal chaos in both cases. However, the catastrophic transition of flows dominated by outer-cylinder rotation can only be understood by accounting for the spatial proliferation of turbulent regions with a statistical approach. We stress the role of the rotation number (the ratio of Coriolis to inertial forces) and show that it determines the lower border for the existence of intermittent laminar-turbulent patterns.