Cracking the boulder-tossing mystery

Storm waves and tsunamis can exert enough force to lift boulders from the base of a cliff and deposit them at its summit. Because such events are exceedingly rare, experimental studies have typically relied on before-and-after observations rather than direct measurements during the event, while computational models often depend on grids or simplifying assumptions that struggle to capture the true physics of boulder transport. Menelaou et al. developed a fully gridless computational method that captures the physics of a wave-displaced boulder at high fidelity.

The method showed that when a highly energetic, steep breaking wave strikes the cliff, it can propel a boulder from the base to the summit. However, vertically clearing the cliff’s height is not enough; the boulder must also experience a brief surge of horizontal momentum strong enough to overcome the returning backwash, and must not have been initially submerged in water.

“Submerged boulders experience significantly reduced horizontal and vertical displacements compared to non-submerged (aerial) boulders, meaning cliff-top deposition is favored only when the boulder is initially on the shore,” said author Frédéric Dias.

The method is based on a computational fluid dynamics method called smoothed particle hydrodynamics, which represents the solid boulder and the liquid water as discrete particles with their own densities, velocities, and accelerations. This approach smoothly simulates the ensuing boulder motion by tracking free surfaces, interfaces, and moving solid boundaries without the constraints of a grid.

Currently, the work is limited to a single boulder with a simple shape on a rectangular cliff. Future work will investigate multiple boulders with more realistic shapes atop more complex cliffs.

Source: “Displacement and deposition of cliff-bottom rocks using smoothed particle hydrodynamics,” by Constantinos Menelaou, Vikram Pakrashi, and Frédéric Dias, Physics of Fluids (2026). The article can be accessed at https://doi.org/10.1063/5.0330036 .