Hydraulic hysteresis in turbulent wakes under a free surface

It is well known that a turbulent wake behind an obstacle placed beneath a free surface can show two completely different flow states. One is a supercritical flow with a discontinuous surface, while the other is a subcritical flow with a smooth surface. In the present study, we aim to quantitatively capture a hydraulic hysteresis around these bistable states. For this purpose, we conduct experiments of the wake behind a square plate placed beneath a free surface, and we measure the velocity fields using particle image velocimetry and the drag force using a load cell. The results show that the hysteresis loop can be captured around the Froude number of unity, both when changing the plate depth at a fixed inflow velocity and when changing the inflow velocity at a fixed plate depth. We also conduct experiments varying the plate size L to show the condition (depth≲0.4L) under which the hydraulic hysteresis appears.