Fractal Dimension of Solar Wind Speed at Different Time Scales Using Box Counting Method

Abstract

Our investigation focused on the analysis of the fluctuations of slow and fast solar winds through the determination of the fractal dimension at different time scales of this ionized flow that escapes from the sun towards the atmosphere. The data used to achieve this goal are high-frequency solar wind speed data covering a twenty-five-year period (1998-2022), directly extracted from the omniweb server database. The box counting method was adopted to calculate the fractal dimension of the solar wind speed. It appears from this study that the frequency of occurrence of the slow solar wind is 78.61% compared to 21.39% for the fast solar wind. The fractal nature of the solar wind speed is dependent on the time scale. For the fast solar wind, the values of fractal dimension vary between 0.65 obtained in 1989 and 0.91 recorded in 2003. As for the slow solar wind, the values of the fractal dimension obtained remain more or less stable with small variations from one year to another. Although the slow solar wind has been shown to be more fractal than the fast solar wind, it appears to have deterministic behavior due to the invariance of its monthly fractal dimension.