So, this is my conjecture (Chapin is silent on this since he was more concerned about the anchor): but I think there are a couple of things going on here. First, the 1852 version has filigree that appears to me to be somewhat indicative of a breaking wave. Second, it also, at that point, replaces a more traditional escutcheon shape (though the preceding image was a 1782 seal, which means that theoretically could’ve occurred at any time over the intervening 70 years).

You can see that in this 1876 image of the State arms from Henry Mitchell’s The State Arms of the Union that the basic pattern of the filigree used by Mitchell around the escutcheon looks a lot like what’s present on this interpretation of the modern seal (which if from Wikipedia and uses Chapin as its source as well). Now, as far as I know, this is original to Mitchell… but it might not be. If you look at the other arms, Mitchell largely uses the same escutcheon shape with the same filigree style. RI’s is the only escutcheon with this particular asymmetrical shape. So it’s possible that Mitchell was reacting to images already out there (the 1852 engraving’s filigree is asymmetrical, but not like this), or he developed his own shape & filigree and that influenced subsequent design here in RI.

FWIW, this filigree is not mentioned in state law for either the arms or for the seal. So they’re completely discretionary to the designer or the administration that commissioned them.