I'm betting that the Egyptian word being translated
as "cataract" is a compound word meaning "falling water".

This would really affect the meaning of utterance 423: (http://www.wyldwytch.com/weavings/reading_room/books/egypt/pyramid.htm)

765a. To say: O Osiris N., take to thyself this thy libation, which is offered to thee by Horus,

765b. in thy name of "He who is come from the cataract"; take to thyself thy natron that thou mayest be divine.

765c. Thy mother Nut has made thee to be as a god to thine enemy (or, in spite of thee), in thy name of "God."

766a. Take to thyself the efflux which goes forth from thee.

766b. Horus has made me assemble for thee the gods from every place to which thou hast gone.

766c. Take to thyself the efflux which goes forth from thee.

766d. Horus has made me count for thee his children even to the place where thou wast drowned.

p. 146

767a. Ḥr-rnp.wi recognizes thee, for thou art made young again, ill this thy name of "Fresh water."

767b. Horus is indeed a soul, for he recognizes his father in thee, in his name of "Ḥr-bȝ-’iti-rp.t."



I'm most interested in anything anyone knows about the Egyptian
word and its derivation. I'm also interested in whether or not
the hieroglyphs in this particular case vary from other uses for
the term or words.

It doesn't appear that the referant is N so it's probably Osiris.

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Man fears the pyramid, time fears man.