Calculating catastrophe
On March 11, 2011, a magnitude 9.0 earthquake off the Sanriku coast of Japan generated a catastrophic tsunami. Waves reached run-up heights of 40 meters in some areas, inundating over 400 square kilometers of land along the Pacific coast. Amid the widespread destruction, geologists observed something curious: the water had moved immense boulders, some weighing tens of tons, for hundreds of meters. This presented a complex physics problem. By studying these displaced rocks, scientists can calculate the immense forces the wave unleashed, measuring the tsunami's force.
Researchers use a set of hydrodynamic equations to estimate the minimum flow velocity needed to move a coastal boulder. These calculations must account for multiple forces acting on the rock. The primary forces are drag, which is the force of the water flowing against the boulder, and lift, an upward pressure created by the moving fluid. Opposing these are the boulder's submerged weight and the friction between it and the ground. A boulder begins to slide when the hydrodynamic forces exceed the resisting forces. At Hoshiyama beach on the Sanriku coast, one large boulder with a long-axis of 7.35 meters was moved by the 2011 tsunami. Simulations suggest the water there reached a maximum velocity of 6.51 meters per second, just enough to initiate motion according to the equations.