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

Abstract

[1] Probability density functions (pdfs) for time-delayed differences of the solar wind proton density np are shown to be approximately self-similar over the range of timescales from ∼90 to 1100 s with an approximate scaling exponent γ = 0.274. The density pdfs are found not to be self-similar over the expanded range of timescales from 90 to 104 s in the spacecraft frame. Pdfs for time-delayed differences of the kinetic energy density ρV2 are found not to be self-similar over either of these two time ranges. The observed self-similar scaling of the proton density is important because it implies that the nonlinear evolution of this quantity in the inertial range of the turbulence is devoid of intermittency effects. These conclusions are based on the analysis of 10 years (a) of data from the Solar Wind Experiment on board the Wind spacecraft covering the time period from 1995 to 2004 and containing approximately 2.5 × 106 data points. Two types of analyses are performed. First, a graphical analysis is used to see whether the rescaled pdfs all lie on a common curve. Then, an analysis of low-order structure functions is performed to see if the scaling properties of the structure functions are consistent with self-similar scaling. Ideally, the results of the pdf scaling analysis and the structure function analysis should both produce the same value of the scaling exponent. Because structure functions are influenced by the presence of outliers in the data, special analysis techniques have to be used to extract the scaling behavior. The special techniques employed here are found to be of limited practical utility because of difficulties in obtaining demonstrable convergence of the scaling exponents.