Avalanching systems under intermediate driving rate

The paradigm of self-organized criticality (SOC) has found application in understanding scaling and bursty transport in driven, dissipative plasmas. SOC is, however, a limiting process that occurs as the ratio of driving rate to dissipation rate is taken to zero. We consider the more realistic scenario of finite driving rate. Similarity analysis reveals that there is a control parameter RA which is analogous to the Reynolds number RE of turbulence in that it relates to the number of excited degrees of freedom, that is, the range of spatio-temporal scales over which one finds scaling behaviour. However for avalanching systems the number of excited degrees of freedom is maximal at the zero driving rate, SOC limit, in the opposite sense to fluid turbulence. Practically, at finite RE or RA one observes scaling over a finite range which for turbulence, increases with RE and for SOC, decreases with increasing RA, suggesting an observable trend to distinguish them. We use the BTW sandpile model to explore this idea and find that whilst avalanche distributions can, depending on the details of the driving, reflect this behaviour, power spectra do not and thus are not clear discriminators of an SOC state.