  Two laboratory scale experiments of dry and under-water avalanches of
non-cohesive granular materials are investigated. We trigger solitary waves and
study the conditions under which the front is transversally stable. We show the
existence of a linear instability followed by a coarsening dynamics and finally
the onset of a fingering pattern. Due to the different operating conditions,
both experiments strongly differ by the spatial and time scales involved.
Nevertheless, the quantitative agreement between the stability diagram, the
wavelengths selected and the avalanche morphology reveals a common scenario for
an erosion/deposition process.
