gully

/ˈɡʌli/
noun
  1. A narrow channel or ditch cut by running water, especially on a hillside or in soft ground.
    • After the heavy rain, a deep gully formed along the side of the dirt road.
    • The hikers followed a dry gully that led down to the riverbed.
    • Farmers built small dams across the gully to slow down erosion.