“We know these big waves cannot get into shallow water,” said David W. Wang of the Naval Research Laboratory, the science arm of the Navy and Marine Corps. “That’s a physical limitation.”

Image STORM SURGE The chief engineer of the Stolt Surf took photographs as the tanker met a rogue wave in 1977. The deck, nearly 75 feet above sea level, was submerged. Credit... Karsten Petersen

By one definition, the titans of the sea rise to heights of at least 25 meters, or 82 feet, about the size of an eight-story building. Scientists have calculated their theoretical maximum at 198 feet — higher than the Statue of Liberty or the Capitol rotunda in Washington. So far, however, they have documented nothing that big. Large rogues seem to average around 100 feet.

Most waves, big and small alike, form when the wind blows across open water. The wind’s force, duration and sweep determine the size of the swells, with big storms building their height. Waves of about 6 feet are common, though ones up to 30 or even 50 feet are considered unexceptional (though terrifying to people in even fairly large boats). As waves gain energy from the wind, they become steeper and the crests can break into whitecaps.

The trough preceding a rogue wave can be quite deep, what nautical lore calls a “hole in the sea.” For anyone on a ship, it is a roller coaster plunge that can be disastrous.

Over the centuries, many accounts have told of monster waves that battered and sank ships. In 1933 in the North Pacific, the Navy oiler Ramapo encountered a huge wave. The crew, calm enough to triangulate from the ship’s superstructure, estimated its height at 112 feet.

In 1966, the Italian cruise ship Michelangelo was steaming toward New York when a giant wave tore a hole in its superstructure, smashed heavy glass 80 feet above the waterline, and killed a crewman and two passengers. In 1978, the München, a German barge carrier, sank in the Atlantic. Surviving bits of twisted wreckage suggested that it surrendered to a wave of great force.