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Nucleation and growth of dry grain avalanches -- (undated)
Jean Rajchenbach , (Univ. P.et M.Curie) jer@ccr.jussieu.fr
First, the main features displayed by dry grain avalanches in laboratory experiments are recalled. Two regimes must be distinguished. The fist regime corresponds to the spontaneous triggering of avalanches, for angle slopes of the same magnitude as the maximal angle of repose theta_{c}. The rear front is shown to propagate upwards with velocity equal (in absolute value) to the downward depth-averaged velocity of the flowing layer, while the head front propagates downwards with a velocity equal to twice the depth-averaged velocity of the avalanche. The second regime corresponds to the external forcing of avalanches, for slopes slightly smaller then theta_{c}. In that last case, the rear front propagates downwards with a velocity equal to the depth-averaged velocity of the avalanche. We suggest simple mechanisms which quantitatively account for the observed dynamical properties. Then we propose an analytical derivation aiming at accounting for the avalanche growth as a function of the time for the two different regimes. The two different solutions, which proceed from a singularity in the rear front velocity as a function of the slope, resemble very closely the experimental observations.