Solar turbulence from sunspot records

Abstract

ABSTRACTIt is generally assumed that coupling between the turbulent flow and the magnetic field at the top of the Sun's convection zone leads to a Kolmogorov cascade of kinetic to magnetic energy. An inertial range and a slope value close to −5/3 have been recognized in a log–log diagram of power spectral density versus frequency (or period). However, published values of the slope have large uncertainties and the inertial period range is limited to 0.1 s to 2 yr. We have applied an adapted version of the singular spectrum analysis (SSA) method to the series of (quasi-) daily sunspot numbers ISSN (an indirect way of monitoring solar activity) from 1868 to 2019. The log–log diagram of ISSN variance of SSA components versus frequency displays an inertial slope value of −1.66 ± 0.16 and an inertial range from about 4 to 100 yr. This is consistent with the existence of Kolmogorov turbulent behaviour in the Sun's convection zone.