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From the starting point of the well known Reynolds number of fluid turbulencewe propose a control parameter $R$ for a wider class of systems includingavalanche models that show Self Organized Criticality (SOC) and ecosystems. $R$is related to the driving and dissipation rates and from similarity analysis weobtain a relationship $R\sim N^{\beta_N}$ where $N$ is the number of degrees offreedom. The value of the exponent $\beta_N$ is determined by detailedphenomenology but its sign follows from our similarity analysis. For SOC,$R=h/\epsilon$ and we show that $\beta_N<0$ hence we show independent of thedetails that the transition to SOC is when $R \to 0$, in contrast to fluidturbulence, formalizing the relationship between turbulence (since $\beta_N>0$, $R \to \infty$) and SOC ($R=h/\epsilon\to 0$). A corollary is that SOCphenomenology, that is, power law scaling of avalanches, can persist for finite$R$ with unchanged exponent if the system supports a sufficiently large rangeof lengthscales; necessary for SOC to be a candidate for physical systems. Wepropose a conceptual model ecosystem where $R$ is an observable parameter whichdepends on the rate of throughput of biomass or energy; we show this has$\beta_N>0$, so that increasing $R$ increases the abundance of species,pointing to a critical value for species 'explosion'.

Control parameters in turbulence, Self Organized Criticality and ecosystems