Bifurcation induced by the aspect ratio in a turbulent von Kármán swirling flow

Abstract

We evaluate the effect of two experimental parameters on the slow dynamics of a Von-Kármán swirling flow driven by two propellers in a closed cylinder. The first parameter is the inertia momentum 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 propellers 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 Γ = H/D. A bifurcation of the shear layer position appears. Whereas for low Γ the shear layer position has a smooth evolution when turning the asymmetry between the rotation frequency of the propellers, for high Γ the transition becomes abrupt and a symmetry breaking appears. Secondly we observe that the spontaneous reversals already observed in this experiment for Γ = 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.

Production and dissipation of turbulent fluctuations close to a stagnation point

“…Conditioning the dataset on the two states, we have reconstructed corresponding mean flows and demonstrated a rotation of π/2 around the axis of rotation. Consequently, the present bistability is different from those observed in similar flows produced in a cylindrical vessel for which the different states mirror each other in a reflexion about the midplane z = 0 [16][17][18]25]. Further work is needed to fully characterize the reversals and their temporal dynamics and to test modeling approaches typically used in confined flows or more generally techniques pertaining to turbulent multi-stability such as [16,26,27].…”

Experimental lateral wall boundary layer behavior of a differentially rotating split-cylinder flow

“…When the fluid is in a laminar regime, the flow created can generate coherent structures that have been analyzed numerically and experimentally [10,11]. In the turbulent regime, the global recirculation can destabilize, and a rich dynamics appears [8,9,12,13]. Apart from the interest as a fundamental problem of fluid mechanics, the presence of instabilities on these flows can affect other processes: these flows have been used experimentally to generate the dynamo action [14,15], and it has been observed that the presence of instabilities can significantly affect the threshold of this effect [16,17].…”