Here’s a fascinating physics video for your amusement and edification:
I think the video explains what is going on pretty well, but if you want more information (including some connections with other bits of physics) you can look at this paper (whence I’ve nicked the following pictures and description).
Basically what is happening is that the motion of the plate through the water in the pool creates a connected pair of Rankine Vortices, rotating in opposite directions. The kinetic energy and the angular momentum the vortices quickly decay so the structure turns into a pair of dimpled singular surfaces called Falaco Solitons. Although unstable, these structures can survive for several minutes if the water in the pool is otherwise still:
Severing the thin, string-like, structure that connects the two dimples will make them vanish extremely rapidly.
The spooky-looking black discs you can see apparently floating on the surface…
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