Hysteretic transition from laminar to vortex shedding flow in soap films

Abstract

There are different ways for fluid flow to become turbulent, but usually many instabilities take place before that. Among these instabilities the transition from laminar flow to vortex shedding carries significant practical importance. Here we study a flow, where at high enough flow rates, vortices are generated by a fixed obstacle (cylinder), which penetrates a flowing, quasi-two dimensional soap film. We present experimental results that demonstrate that the transition from laminar flow to a periodic Kármán vortex street can be hysteretic, i.e. changing the mean flow rate $\bar V$ vortices can survive at velocities lower than the velocity needed to generate them. This is an unexpected result since 3D experiments are well described by the Hopf equation, which is incompatible with hysteresis. Beyond that, our data cannot be satisfactorily fitted by the generic model of hysteresis, i.e. the 5th order Landau equation. It is found that a phenomenological model describes our experimental findings very well. Evidences are presented that wetting properties of the rod, mechanical instabilities (i.e. vibrations) of the setup, and the effect of the surrounding air are not the cause of the hysteresis. To reduce three dimensional effects, the rod was replaced by a disk having a thickness roughly eight times that of the film. The replacement of the rod by a disk increases the gap width and the shedding frequency. Behaviour of the system (for instance the unstable trajectory) in the hysteretic gap is investigated by means of transient measurements.