Can fluid dynamics offer insights into quantum mechanics?

Can fluid dynamics offer insights into quantum mechanics?: In Couder’s system — which Bush plans to explore further at MIT — a fluid-filled tray is placed on a vibrating surface. The intensity of the vibrations is held just below the threshold at which it would cause waves — so-called Faraday waves — on the surface of the fluid. When a droplet of the same fluid is placed on the surface, it’s initially suspended on a cushion of air. Although the surface of the fluid appears perfectly placid, the vibration of the tray flings the droplet upward before the cushion of air dissolves, and the droplet begins bouncing. The bouncing causes waves, and those waves, in turn, propel the droplet along the surface. Bush and Couder call these moving droplets “walkers.”
“One of their first experiments involved sending walkers towards a slit,” Bush says. “As they pass through the slit, they appear to be randomly deflected, but if you do it many times, diffraction patterns emerge.” That is, the droplets strike the far wall of the tray in patterns that reproduce the interference patterns of waves. “Their system is a macroscopic version of the classic single-photon diffraction experiments,” Bush says.
Wave-borne fluid droplets mimic other quantum phenomena as well, Bush says. One of these is quantum tunneling, subatomic particles’ apparent ability to pass through barriers. A walking droplet approaching a barrier across the tray will usually bounce off it, like a hockey puck off the wall. But occasionally, the droplet will take enough energy from the wave that it hops right over the barrier.