The Captain's Vengeance by Dewey Lambdin

Sailing in the Caribbean, Captain Alan Lewrie, RN, is once again pursuing a chimera.
A rich French prize ship he'd left at anchor at Dominica has gone missing, along with six of his sailors. What starts as a straightforward search for it, and them, from Hispaniola to Barbados, far down the Antilles, leads Lewrie to a gruesome discovery on the Dry Tortugas and to a vile cabal of the most pitiless and depraved pirates ever to sail under the "Jolly Roger" . . . and the suspicion that one of his trusted hands just may be the worst of them all!