By turbulence I mean a chaotic field full of eddies. As far as I'm aware this is the state of most fluids, like the airflow in an room, unless effort has been taken to make the flow laminar. Shouldn't these movements be visible everywhere on the surface of bodies of water, as distorting their ripples and waves?
Sometimes vortices do appear, but just a few at a time under specific conditions and not in the same chaotic fashion as turbulence would suggest.
A possible explanation I can think of is that momentum carried through turbulence is negligible compared to surface tension and forces creating waves. So disturbances don't deform the surface even though they exist a short distance below it.