Self-similar stochastic processes in solar wind turbulence

Solar wind data is used to estimate the autocorrelation function for the stochastic process x(τ) = y(t + τ) − y(t), considered as a function of τ, where y(t) is any one of the quantities B²(t), n_p(t)V²(t), or n_p(t). This process has stationary increments and a variance that increases like a power law τ^2γ where γ is the scaling exponent. For the kinetic energy density and the proton density the scaling exponent is close to the Kolmogorov value γ = 1/3, for the magnetic energy density it is slightly larger. In all three cases, it is shown that the autocorrelation function estimated from the data agrees with the theoretical autocorrelation function for a self-similar stochastic process with stationary increments and finite variance. This is far from proof, but it suggests that these stochastic processes may be self-similar for time scales in the small scale inertial range of the turbulence, that is, from approximately 10 to 10³ s.