Bifurcation induced by the aspect ratio in a turbulent Von-K\'arm\'an swirling flow

TL;DR

This study investigates how the aspect ratio influences shear layer bifurcations and reversals in a turbulent Von-Kármán swirling flow, revealing a critical aspect ratio where flow symmetry and dynamics change abruptly.

Contribution

It demonstrates that the aspect ratio induces a bifurcation in shear layer position and affects flow reversals, with no significant effect from propeller inertia modifications.

Findings

Shear layer position bifurcates with aspect ratio changes.

Flow reversals occur only within specific aspect ratio ranges.

Shear layer dynamics are governed by mean flow structure and turbulent fluctuations.

Abstract

We evaluate the effect of two experimental parameters on the slow dynamics of a Von-K\'arm\'an swirling flow driven by two propellers in a closed cylinder. The first parameter is the inertia mo- mentum of the propellers, and the second parameter is the aspect ratio, i.e. the distance between the propellers $H$ divided by the diameter $D$. We use a cell with a fixed diameter $D$ but where the distance between the propellers can be turned continuously and where the inertia from the pro- pellers can also be changed using different gears. No change on the dynamics is observed when the momentum of inertia is modified. Some dramatic changes of the shear layer position are observed modifying the aspect ratio $\Gamma=H/D$. A bifurcation of the shear layer position appears. Whereas for low $\Gamma$ the shear layer position has a smooth evolution when turning the asymmetry between the rotation frequency of the propellers, for high $\Gamma$ the transition becomes abrupt and a symmetry breaking appears. Secondly we observe that the spontaneous reversals already observed in this ex- periment for $\Gamma=1$ [de la Torre & Burguete PRL 99, 054101 (2007)] exist only in a strait window of aspect ratio. We show using an experimental study of the mean flow structure and a numerical approach based on a Langevin equation with coloured noise that the shear layer position seems to be decided by the mean flow structure whereas the reversals are linked to the spatial distribution of the turbulent fluctuations in the cell.