From Code Girls, by Liza Mundy (Hachette, 2017), Kindle pp. 280-281:
After the carnage of 1942 and early 1943, the Allies had seen a stunning turnaround in the Atlantic. By September 1943, most U-boats had been swept from the Atlantic waters. This was thanks not only to the new high-speed bombes but also to a host of other Allied war measures: advances in radar, sonar, and high-frequency direction finding; more aircraft carriers and long-range aircraft; better convoy systems. The Allies changed their convoy cipher, and Dönitz could no longer read it. The tables turned. During the summer, American hunter-killer units used code breaking along with other intelligence to find and sink big German submarines that were sent out to refuel U-boats. These refuelers were known as milch cows, and between June and August, American carrier planes sank five. In October, they finished off all but one. The refuelers were critical to the U-boats’ ability to stay so far away from their home base, and as the milch cows went down, the U-boats began to drift homeward.
There was always the chance, however, that the U-boats could come back. And they did try. In October 1943, the U-boats reappeared. But now the costs were punishingly high. For every Allied merchant vessel sunk, seven U-boats were lost. Now Dönitz was the one who could not build boats fast enough to replace those he was losing. In November, thirty U-boats ventured into the North Atlantic and sank nothing. The U-boats began lurking elsewhere, clustering around the coast of Britain, hoping to intercept materiel brought in for an anticipated invasion of France. Dönitz was always trying to innovate the U-boats, adding a Schnorchel that enabled them to remain submerged longer. He was willing to sacrifice his boats, and his men, and kept the U-boats in the water even as a way to tie up Allied resources.
But it was a losing battle. In May 1944, the Allies sank half the U-boats in operation—more than the Germans could replace. More than three-quarters of the U-boat crews were killed, suffering terrible watery deaths. The women in the tracking room were privy to the full immensity and horror.
By now the British had indeed handed over the four-rotor bombe operations to the Americans. After the war, a U.S. Navy file was made of messages from grateful—and gracious—British colleagues. “Congratulations from Hut six on colossal… week,” said one missive from Bletchley. An internal British memo acknowledged that “by half way through 1944” the Americans “had taken complete control of Shark and undoubtedly knew far more about the key than we did.”