Sorry to enter the thread so late. I have been hovering on it for a while because a fine Manx harper, Charles Guard, called a track on his album (originally on the Irish Claddagh label, now available on CD through Green Linnet) 'The Song of the Water Kelpie'.
Although I played on that particular track, I have to say that I disagree with Charles's naming of it.
On the west coast of Mann is a village called Dalby - pronounced either Delby or Dawby. There is a story of a figure arriving through the mist off the coast. He sang a song as he appeared, but no-one could understand the lyrics, if there were any, but the tune became known as the Arrane Ghelby, The Song of Dalby. Charles Guard seems to have taken this as Arrane Kelpie, or some such.
The figure who sang this song was either someone in a boat, or, in line with other mythological traditions, someone who was, in fact, as one or part of the boat. People were said to have tried to row out and hear the lyrics, but the tune was all they got.
There are 20th century words in Manx Gaelic added to this beautiful tune. There are schools of thought which link this tune with very old Scandinavian traditions on the one hand, and Goedelic traditions on the other.
As Sylvia Wood has suggested a Manx provenance, I thought it as well to throw in my two-pennyworth, having not come in earlier as I thought it was related to a different tradition - as I'm sure the Oran Tlaidh an Eich-Uisge probably actually does.