Self-similar scaling of magnetic energy in the inertial range of solar wind turbulence

Abstract

Turbulent magnetic field fluctuations in the solar wind undergo an energy cascade in the inertial range with a characteristic Kolmogorov frequency spectrum f⁻⁵/³. Using magnetic field measurements from the Wind and ACE spacecraft at 1 AU in the ecliptic plane, probability distributions (PDFs) of time-delayed differences of magnetic energy density B²(t) are shown to exhibit an approximate self-similar scaling for time lags τ in the inertial range of the turbulence, that is, from approximately 10 to 1000 s. The scaling is characterized by a single scaling exponent γ, the Hurst exponent, and a universal PDF that is independent of scale for timescales in the inertial range. It is shown that the scaling exponent and the form of the universal PDF change with the 11-year solar cycle due to the changing nature of the turbulence. The timescale for these changes is roughly estimated to be on the order of 1 or 2 years. Studies of low-order structure functions are performed in an attempt to corroborate the self-similar scaling of the PDFs. It is found that the structure functions do not scale in a self-similar manner indicating that the PDFs are not truly self-similar. Therefore the claimed self-similar scaling of the PDFs is only a rough approximation.