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We present the time and space evolution, i.e., stability properties, of gravity currents flowing downslope over an erodible sea bottom. This bed consists of noncohesive fine-grained sediments, entrainment of which can increase the current density. To schematize such a complex interaction, we assume that initially the current is slow, such that no sediment entrainment occurs. At a fixed time an external forcing is applied, giving rise to hydrodynamic perturbations. These can increase the water velocity, generate turbulence, and in turn entrain bottom sediments, further increasing the water velocity. In our model turbulent energies are not considered explicitly since we assume that density variations, ultimately due to turbulent bottom erosion or deposition, are given by an empirical formula discussed by Itakura and Kishi (1980), Parker et al. (1986), and Garcia and Parker (1993). A complex, but solvable, equation is thus obtained, in which both time and space variability for a realistic two-layer model of gravity currents flowing over an erodible slope below less dense ambient water are considered. On mathematical grounds, this consists in a diffusion equation, but with a peculiar type of nonlinear “time-delayed” evolution. Comparison with the experimental data suggests that the most interesting quantity is probably the “ignition” time, i.e., the time necessary for an external forcing to generate nonlinear explosive effects and sediment entrainment. Finally a numerical study of the evolution of current thickness supports the evidence of these nonlinear effects.

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