Relations of 1/f and 1/f2 power spectra to self-organized criticality

Power law distributions of burst duration and interburst interval in the solar wind: turbulence or dissipative self-organized criticality?

We calculate the probability density functions P of burst energy e, duration T, and interburst interval tau for a known turbulent system in nature. Bursts in the Earth-Sun component of the Poynting flux at 1 AU in the solar wind were measured using the MFI and SWE experiments on the NASA WIND spacecraft. We find P(e) and P(T) to be power laws, consistent with self-organized criticality (SOC). We find also a power-law form for P(tau) that distinguishes this turbulent cascade from the exponential P(tau) of ideal SOC, but not from some other SOC-like sandpile models. We discuss the implications for the relation between SOC and turbulence.