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

Abstract

Abstract. Toma hills are the perhaps most enigmatic morphological feature found in rock avalanche deposits. While it was already 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 Voellmy's rheology, which was recently developed for explaining 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, falling back to Coulomb friction may cause a sudden increase in friction. Material accumulates in the region upstream of a point where this happens. In turn, high velocities may persist for some time in the downstream and lateral range, resulting in a thin deposit layer finally. In combination, both processes generate more or less isolated hills with shapes and sizes similar to toma hills found in real rock avalanche deposits. So the modified Voellmy rheology suggests a simple mechanism for the formation of toma hills.