Rapids and several other "white water" systems could be typical examples of turbulent motion. To describe such flows the Navier-Stokes equations must be extended by terms describing the surface tension and other features of a multiphase flow. I have no doubt that this can get really ugly at "still simple" approximation.
My question is: does the surface tension attenuate the turbulent behavior or amplify it? I assume that there isn't simple yes/no answer and that it would require a discussion of energies and scales.