Admiralty law is expressly acknowledged by the Constitution and is not antithetical to the common law. Admiralty jurisdiction is one of the jurisdictions expressly conferred on the federal - common law - courts. Admiralty law rarely has anything to do with martial law, but mostly has to do with what happens when a ship is damaged or a cargo is screwed up.
And formerly was confined to domestic American matters involving states which had coastal areas, but more recently, has been *reinterpreted* by the federal courts to include and states which have a federal waterway [river] as a boundary of that state, or adjoining any other "Federal Waterway". The Lake of the Ozarks, for instance....