From annular cavity to rotor-stator flow: nonlinear dynamics of axisymmetric rolls

TL;DR

This paper investigates the nonlinear dynamics of axisymmetric rolls in rotor-stator flows by deforming the flow into an annular configuration to understand the transition to unsteadiness and chaos as functions of Reynolds number.

Contribution

It introduces a homotopy approach to analyze flow transitions, revealing the influence of curvature and modal interactions on flow stability and chaos onset.

Findings

Identification of the critical Reynolds number for flow instability.

Discovery of a new nonlinear mechanism for roll pairing.

Observation of subcritical chaotic states emerging with increased curvature.

Abstract

Spatio-temporally complex flows are found at the onset of unsteadiness in (axisymmetric) rotor-stator turbulence in the shape of concentric rolls. The emergence of these rolls is rationalised using a homotopy approach, where the original flow configuration is continuously deformed into a simpler, better understood configuration. We deform here rotor-stator flow into an annular flow, thereby controlling curvature effects, and we investigate numerically the transition scenarios as functions of the Reynolds number. Increasing curvature starting from the planar limit reveals a clear path towards a subcritical scenario as a function of the Reynolds number. As the rotor-stator configuration is approached, supercritical branches shift to increasing Reynolds number while a subcritical branch of chaotic states takes over. Modal selection in the supercritical scenario involves the competition between two modal families. It rests on a specific radial localisation property of all eigenmodes, linked to the space-dependent convective radial velocity which intensifies as curvature is increased. A new nonlinear mechanism for the pairing of rolls is proposed based on multiple resonances. The critical point where the original rotor-stator flow loses its stability to axisymmetric perturbations is identified for the first time for the geometry under study.