  In the present article we consider the problem of underwater avalanches
propagating over moderate slopes. The main goal of our work is to investigate
the avalanche front velocity selection mechanism when it propagates downwards.
In particular, we show that the front velocity does not depend univocally on
the mass of sediments. This phenomenon is investigated and explained in our
study. Moreover, we derive from the first principles a depth-averaged model.
Then, we assume that sediments are uniformly distributed along the slope. In
this case, they can be entrained into the flow head and a self-sustained regime
can be established. One of the main findings of our study is that the avalanche
front velocity is not unique due to a hysteresis phenomenon. We attempt to
explain this phenomenon using dynamical systems considerations.
