How did the Proto-Indo-European word *(s)k̑eh₁weros turn into the Latin word "caurus"? How did the long 'e' turn into 'a'? I suppose it was some form of an ablaut that turned long 'e' into long 'o', but long 'o' doesn't regularly turn into 'a' in Latin. Besides, it's a short 'a' in "caurus", it's a part of a "au" diphthong, and we know that because there are some Late Latin attestations of that word as "corus". As far as I know, "au" in Latin usually comes from "h₂ew", as in "aurum" (gold) < *h₂ews.
1 Answer
The Latin word continues a form with a zero-grade in the root and an e-grade in the suffix: *k̑h̥₁u̯-er-o-s. The laryngeal is vocalic, and any vocalic laryngeal yields a in Italic. Proto-Italic *kaweros then regularly gives Latin caurus.
Lithuanian šiaurė 'north' continues a *k̑eh₁u̯-r-o-s, with a full-grade in the root and a zero-grade in the suffix, and Slavic (e.g. OCS sěverъ 'north') seems to continue a double full-grade *k̑eh₁u̯-er-o-s; thematic nouns don't, as a rule, undergo ablaut, so all of these forms presumably represent a relatively late thematisation of a proterodynamic athematic noun (or conceivably a keššar-type noun, if you're Alwin Kloekhorst, though those tend to be more fundamental vocabulary), which would have had *k̑eh₁u̯-r- in some cases (notably the nominative singular) and *k̑h̥₁u̯-er- in others. Different languages built their thematic noun on different forms, and some kind of contamination created a Frankenstein form in Slavic.