Self-similar properties of avalanche statistics in a simple turbulent model

In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterized by two well-defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time t(w) followed by abrupt avalanche-like energy drops of sizes S due to strong intermittent fluctuations 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 and numerically checked that their scaling properties are related based on a simple, but non-trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.