A burbling stream.

This little stream certainly was producing some lovely burbling sounds with all of the rain we’ve had recently.
The verb burble captures both the movement of the water and the sound it makes as it moves. You could also say that a brook or stream or river babbles or ripples or even trickles. The word burble was first used in the 1300's, and it probably comes from an imitation of the sound a rippling, bubbling brook makes.