The formation of waves is caused by the deceleration of moving water into slack water or in to more slowly moving water. As water comes down from a drop it enters a space that is occupied by stagnant water. The immediate result is that it tries to displace the stagnant water and since there is no place for the water to go it rises upward briefly creating a standing wave.
For a classic example of this see the Himalaya rapid on Chile's Futaleufu River. Here the river, moving upwards of 40-50 kph enters a deceleration pool creating some of the most massive waves in the hemisphere. Check out the video section:
www.exchile.com/guide/index.php/Himalayas
In the case of Hydraulics the effect is more pronounced. The water upstream has a definite downward momentum and flows under the slackwater causing the slackwater to rise and then fall backward. The physics are a bit more complicated but are similar to the creation of a backward current in an eddy. In the case of a hydraulic this backward current occurs over the surface of the water. (ie, the water needs someplace to go after it rises) A great example of this can be found here:
www.dailymotion.com/video/xxmn1_painkiller-a-hawai-sur-loch
hope this helps...
PS.. the water behind a rock is definitely stagnant.