Until 2002, these giant creatures were seen only occasionally in Japanese waters. But for the past five years, they have been swarming every year into the Sea of Japan, the water that separates Japan from mainland Asia. During the biggest invasion so far, in 2005, an estimated 500 million jellyfish — not yet mature — drifted in each day.

The Japanese government is doing what it can. It tracks the progress of jellyfish as they swarm through the Sea of Japan, urging trawlers to steer clear of them. The Japanese harvest some jellyfish to eat. Jellyfish can be boiled and added to salads — though smaller varieties are said to be more tender and tasty.

Trying to win converts, the fisheries ministry has drawn up a manual with tips on cooking with giant jellyfish. Menus include jellyfish-flavored biscuits, jellyfish soaked in rum and a dessert of jellyfish chunks in coconut milk.

One coastal firm, Tango Jersey Dairy, has for the past three years produced 2,000 or 3,000 cartons of vanilla-and-jellyfish ice cream. The jellyfish is soaked overnight in milk to reduce its smell, and is then diced. Fumiko Hirabayashi, a director of the dairy, says the jelly cubes are slightly chewy. Jellyfish is also getting publicity in women’s magazines because it contains collagen, a protein used in cosmetics.

“We think it’s important to use local ingredients,” says Mrs. Hirabayashi. “And this has now become a local ingredient.”

Scientists have various ideas about what causes the outbreak. One has devised a computer model of ocean currents that suggests the jellyfish are breeding off the Chinese coast near the mouth of the Yangtze River. One theory is that pollution, perhaps linked to industrialization in China, is helping create more algae in the sea. The algae are food for plankton, which is food for jellyfish.

One fear among scientists is that the creatures are multiplying in a “jellyfish spiral.” Shinichi Uye, a leading jellyfish researcher at Hiroshima University in western Japan, thinks overfishing off China has led to fewer plankton-eating fish, leaving more plankton for the jellyfish to suck up. This growing army of jellyfish then also eats fish eggs, resulting in even fewer fish.