I've noticed these white ripples will appear on the map. The spots are temporary, with them disappearing and new ones appearing occasionally:
What do these nearby white ripples mean?
I haven't been able to figure out what they are since standing near or on top of them gets no reaction, nor does tapping them. I assumed they were “sonar pings” of nearby pokemon because of the way they ripple when your personal circle hits them, but no pokemon have appeared.
Also since researching this question turned up that it's rustling leaves on the map that represents nearby pokemon, I'm guessing this must be something else?