Abstract

In fluid turbulence a single control parameter, the Reynolds number R_E, which is a function of macroscopic system variables is sufficient to quantify the transition from ordered (laminar) to disordered (turbulent) flow. We suggest that a wider class of systems has this property, including Self Organized Criticality (SOC) and ecosystem models for species abundance. These systems can all be driven into a state with defining characteristics: they have many degrees of freedom (d.o.f.); are driven, dissipating and out of equilibrium; are on average in a steady state; and show scaling over a large dynamic range. The Reynolds number expresses the number of d.o.f., or energy carrying modes in the system. For avalanche models exhibiting SOC , d.o.f. refer to avalanche sizes and the Reynolds number R_A that we identify is simply the well known ratio of the driving rate to system dissipation rate. The SOC slowly driven interaction dominated limit is reached by taking R_A to zero; we show this maximizes the number of d.o.f. in the opposite sense to fluid turbulence. This result clarifies the much debated relationship between turbulence and SOC . In ecosystems, the Reynolds number R_B that we propose depends on the rate at which biomass, or energy, is supplied to, and is removed from, an ecosystem. As R_B increases so does the abundance of species, or d.o.f., as in fluid turbulence. This points to the possibility of a critical value of the Reynolds number at which the onset of diversification of species occurs.