The Collaborative International Dictionary of English v.0.48:

Wady \Wad"y\, n.; pl. Wadies. [Ar. w[=a]d[imac] a valley, a
   channel of a river, a river.]
   A ravine through which a brook flows; the channel of a water
   course, which is dry except in the rainy season.
   [1913 Webster]