Not the familiar Northumberland tune of the same title but a tune from Kerr's Merry Melodies
Kerr calls it 'Salmon Tails Up the Water' (don't let the title or the format of Kerr's collections deter you; there's some great music in those books)
This as it stands is not a pipe tune, but it is so clearly in the pipe idiom that the little adjustments necessary are well worth while.
Another version of what looks like the same tune appears in the Rook manuscript from Cumberland, (N.W England), from the 1830's: Rook's title is simply 'Salmon Tails'
Rook's tune seems to be a bit incoherent in the closing bars of the second strain; you might want to treat the final bar as a second time bar, or omit bar 3, or just play it as written (and leave the dancers to sort it out).
That's what I wrote originally; further thought leads me to suspect that Rook [whose manuscript is sometimes rather erratic] has silently employed a device that appears in 19th century highland collections where bars 3 and 4 of the 2nd strain are marked as '1st time' and '2nd time' respectively; play bars 1,2,3,&5 the first time and bars 1,2,4 & 5 on the repeat.
The intriguing thing about this tune title is that it might just be the one referred to by Robert Chambers when describing his meeting with olf James Ritchie, who had been the town piper of Peebles for sixty years when Chambers met him in 1802:
"I suspect that Ritchie had tunes of his own composition, since lost, for there were three called ' Salmon Tails', 'Lyne's Mill Trows', and 'The Black and the Grey' ... which are not to be seen or heard of now-a-days'.
Given that three salmon appear on the coat of arms of Peebles Town, it seems possible that this tune was once the 'town tune' of Peebles.