The Reynolds number was estimated as follows. The diameter of the pole is about 2 inches, so say 50 mm. The flow rate is perhaps 1 meter per second, so 1000 mm/s. The viscosity of water is about 1 mm^2/second. Thus the approximate Reynolds number is 50,000.
Criticisms: we don't have a precise measure of the pole diameter or the flow rate.
More importantly, the supports at the end of the dock are likely making the flow more complicated at the vibrating pols.
Finally, this is not the typical flow past a cylinder since it is a free-surface flow.
The frequency of vibration of the pole is just above one Hertz.