Modeling the formation of toma hills based on fluid dynamics with a modified Voellmy rheology

Abstract

Toma hills are perhaps the most enigmatic morphological feature found in rock avalanche deposits. While it has been proposed that toma hills might emerge from the fluid-like behavior of rock avalanches, there still seems to be no consistent explanation for their occurrence. This paper presents numerical results based on a modified version of the Voellmy rheology, which was recently developed to explain the long runout of rock avalanches. In contrast to the widely used original version, the modified Voellmy rheology defines distinct regimes of Coulomb friction at low velocities and velocity-dependent friction at high velocities. When movement slows down, returning to Coulomb friction may cause a sudden increase in friction. Material accumulates in the region upstream of the point where this happens. In turn, high velocities may persist for some time in the downstream and lateral ranges, ultimately resulting in a thin deposit layer. In combination, both processes generate more or less isolated hills with shapes and sizes similar to those of toma hills found in real rock avalanche deposits. Thus, the modified Voellmy rheology suggests a simple mechanism for the formation of toma hills.