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In this paper, we consider a simplified model of turbulence for largeReynolds numbers driven by a constant power energy input on large scales. Inthe statistical stationary regime, the behaviour of the kinetic energy ischaracterised by two well defined phases: a laminar phase where the kineticenergy grows linearly for a (random) time $t_w$ followed by abruptavalanche-like energy drops of sizes $S$ due to strong intermittentfluctuations of energy dissipation. We study the probability distribution$P[t_w]$ and $P[S]$ which both exhibit a quite well defined scaling behaviour.Although $t_w$ and $S$ are not statistically correlated, we suggest andnumerically checked that their scaling properties are related based on asimple, but non trivial, scaling argument. We propose that the same approachcan be used for other systems showing avalanche-like behaviour such asamorphous solids and seismic events.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Self Similar Properties of Avalanche Statistics in a Simple Turbulent Model