@Lace : I've never heard anyone call it a bayou, usually it's just referred to as the drainage ditch or just the ditch.
I think technically it's an extension of Williams Gully which if you trace it back far enough drains out of Garners Bayou over by the movie theater in Fall Creek.
Although Williams Gully is also sometimes called Williams Bayou on maps so I guess it's not actually incorrect to call it a bayou.