Direct and inverse pumping in flows with homogeneous and non-homogeneous swirl

TL;DR

This paper investigates how meridional recirculations in swirling flows depend on swirl distribution, revealing conditions for flow reversal and implications for turbulence transition, supported by theory, simulations, and experiments.

Contribution

It introduces a theoretical framework linking swirl gradients to flow recirculation directions, validated by simulations and experiments, explaining phenomena in electrolyte flows and turbulence transition.

Findings

Recirculation direction depends on swirl gradient.

Classical 'tea-cup effect' occurs only in quasi-2D flows.

Flow rate scales with swirl gradient.

Abstract

The conditions in which meridional recirculations appear in swirling flows above a fixed wall are analysed. In the classical Bodew\"adt problem, where the swirl tends towards an aysmptotic value away from the wall, the well-known "tea-cup effect" drives a flow away from the plate at the centre of the vortex. Simple dimensional arguments applied to a single vortex show that if the intensity of the swirl decreases away from the wall, the sense of the recirculation can be inverted, and that the associated flow rate scales with the swirl gradient. Only if the flow is quasi-2D, does the classical tea-cup effect take place. This basic theory is confirmed by numerical simulations of a square array of steady, electrically driven vortices. Experiments in the turbulent regimes of the same configuration reveal that these mechanisms are active in the average flow and in its fluctuating part. The mechanisms singled out in this letter provide an explanation for previously observed phenomena in electrolyte flows. They also put forward a possible mechanism for the generation of helicity in flows close to two-dimensionality, which plays a key role in the transition between 2D and 3D turbulence.