Admiralty Courts are courts that operate outside the law. They are not positive law courts but instead are military courts. The key is to look at the flag on the pole when you walk in any courtroom. Any flag that has the yellow fringe is an "army on the march". It is the same flag used by the Commander in Chief of the White House. When you, I, or any regular citizen walks into these courts, we are recognized as the enemy in their courtroom. If you ever notice outside any federal courthouse, as you enter the above plaque reads "Department of War". We are nothing but names of war when walking into their courtroom. It is the same with the state municipal and superior courts as well.
What separates admiralty courts from constitutional courts is that judges don't wear the black robes in constitutional courts and there is no yellow fringe on the flag and positive law is observed.
Admiralty courts apply private law because they conduct courts as a business rather than the process itself. Admiralty courts practice what is called procedural law rather than that of substantial law because law of substance takes "too much time".