To what or whom does the "Shenandoah" in the song by that name refer?

I learned a version of it as a child that begins,

"Oh, Shenandoah, I long to see you;
Way hey, you rolling river;
Oh, Shenandoah, I long to see you;
Way hey, I'm bound away, 'cross the wide Missouri."

And so I always thought that the phrase "you rolling river" meant that the song was addressed to the Shenandoah River (and that "your daughter" mentioned in a later verse was some girl who'd grown up by the river).  Had I learned it first later in life, I might not have been so quick to assume that a song of romantic longing was addressed to a river--but at age about seven, it made perfect sense.

I now need to have that illusion shattered, it seems.  Fire away. . . .

--Jurretta Heckscher

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