I have heard that Drunken Sailor MAY have stolen the melody from Oro Se do Bheatha Abhaile. It makes sense that the melody came from an Irish song since the heyday of the Royal Navy came later in a time when the Dorian mode was largely not used in English music. For those who aren't music nerds, the Dorian mode is a type of minor scale common to Oro Se do Bheatha Abhaila, Drunken Sailor, and Greensleeves.

In the Irish War for Independance, the P. H. Pearse version of the lyrics were sped up to make the song into a fast march. There's a wonderful rendition of this in the film The Wind that Shakes the Barley.

That said, the major difference between Drunken Sailor and Oro Se Do Bheatha Abhaile is the rhythm. For a tinwhistle player (or floutist) to play The Drunken Sailor, the technique used to create the abrupt stops between short notes is called tonguing. This percussive rhythm is not present in Oro Se Do Bheatha Abhaile.

Since I can't put an image of sheet music here, I'll tab out the song for whistle to meet Aaron's request. Parenthesis mean upper octave. You'll have to figure out the rhythm by listening to it. This should work on any tinwhistle or Irish flute. For E Dorian, use a key of D instrument or Tenor D instrument.

11210124 22222642 1121010(5) (5)(4)0(5)011