There is no direct counterpart that is in typical usage.  Use any word that suggests desperation or urgency, if you must use an adverb.  Describing the way the person drank visually would probably be far more descriptive, however. For example: "The traveler sank to her knees, grabbed the jug with both hands, drank the entire contents in one messy draft."

Actually, I would like to add that *ravenous* is not necessarily a term just for hunger; *a ravenous thirst* is a perfectly acceptable phrase.  *Ravenously* also means greedily or in a predatory manner; it is literally derived from the word *raven* (like the bird).  Thanks OED.