The Shoaling Wall

Lituya Bay and the Physics of Shallow-Water Wave Compression

Commercial fisherman Howard Ulrich and his seven-year-old son Sonny were asleep aboard their thirty-eight-foot wooden trolling boat Edrie inside Anchorage Cove in Lituya Bay, Alaska, when the Fairweather Fault ruptured on the night of July 9, 1958. Lituya Bay is a T-shaped glacial fjord ten kilometers long on the rugged coast of the Gulf of Alaska. It connects to the Pacific Ocean only through a narrow, ten-meter-deep boulder sill across its mouth. At the inner head of the bay, the walls of Gilbert Inlet rise more than a kilometer straight out of the water along the active strike-slip fault plane.

Violent shaking made the wooden deck buck beneath Ulrich's feet and woke him at 10:15 p.m. He ran to the wheelhouse and looked five kilometers northeast toward the head of the bay. Roughly 30 million cubic meters of amphibolite and schist—weighing ninety million metric tons—had sheared off the northeastern cliff from an altitude of 900 meters. That entire slab plunged virtually intact into the deep water of Gilbert Inlet. The impact sheared off the front of the Lituya Glacier and threw up a vertical wall of water. The splash stripped virgin Sitka spruce forests down to bare rock on the opposite mountain ridge. Then a towering gravity wave raced down the main trunk of the fjord directly toward Ulrich's anchored boat.

Ulrich started his engine and put a life jacket on his son. When the iron shackle refused to release, he paid out the entirety of his forty-fathom anchor chain and pointed the bow of the Edrie straight into the advancing wall of water. Describing the moment the twenty-five-meter wave front reached his boat near the outer bay, Ulrich later told reporters that the wave never broke over the hull, or they would have died instantly; instead, the swell lifted the boat intact and carried them clean over the tops of the coastal spruce trees. The steel anchor chain snapped like twine. The Edrie surfed high above the submerged forest along the southern shore before riding the backwash safely back into the timber-choked channel.

To understand how a rockfall created a wave that climbed half a kilometer up a mountain wall, United States Geological Survey geologist Don Miller analyzed the hydrodynamics of impulse waves and shallow-water shoaling. When a wavelength $\lambda$ greatly exceeds water depth $h$, a gravity wave travels at a speed controlled solely by the local depth of the basin. Its vertical height $H$ scales across changing channel width $b$ and depth $h$ according to Green's Law of wave shoaling:

In the open Pacific Ocean, where water depth reaches four thousand meters, a tsunami travels at two hundred meters per second—the cruising speed of a commercial jetliner—with a surface height of less than a meter. Inside Gilbert Inlet, the water depth was only 122 meters. There the falling ninety-million-ton rock mass acted as a supersonic piston. It displaced the entire water column faster than gravity waves ($c = \sqrt{9.8 \times 122} \approx 34.6\text{ m/s}$) could carry the water away.

With nowhere to disperse laterally inside the narrow rock-walled fjord, the displaced water piled directly upward into a solitary nonlinear gravity wave. As that immense volume of moving water slammed into the steep bedrock spur opposite the landslide scar, kinetic energy converted directly into gravitational potential energy ($gh$). In August 1958, USGS geologist Don Miller stood at the highest scar on the Gilbert Inlet spur and measured the stripped bedrock at 1,720 feet above sea level, the tallest wave run-up ever recorded on Earth.