A hydraulic jump is a discrepancy in water depths. When water in a stream flows over a rock, for example, the water may reach a very high speed due to the decrease in the height of the water. (This is due to the continuity equation, (initial velocity)(initial height) = (final velocity)(final height).)* If the speed increases greatly, it may exceed the speed that waves propagate at; such a speed is called "super-critical" flow. In this case, a sudden jump in the water's height will occur so that the speed of the water is reduced to sub-critical speed.
The equation that governs this phenomena is:
is called the Froude number, is the speed of the water, is the acceleration due to gravity, and is the depth of the water.
* This is a simplified version of the continuity equation (it is not in integral form).