Fractality of an {MHD} shell model for turbulent plasma driven by solar wind data: A review

The Gledzer-Yamada-Ohkitani MHD shell model is used to describe dissipative events that take place in magnetized plasmas. In this review we summarize a series of works aimed to characterize the fractal features of the GOY shell model using various choices of the forcing terms, as an attempt to model the behavior of the Earth's magnetosphere driven by the solar wind. Usually, stochasticity in the shell model is included by using the solution of a Langevin equation in its forcing terms. We compare that method with cases where solar wind data spanning the full 23rd solar cycle is used to build the forcing terms of the shell model. Correlations are found between the fractal dimension of the forcing and the energy dissipation rate obtained from the shell model description. This shows that the GOY shell model is able to respond to statistical variations on the driving. Also, it shows that the fractal dimension, although it is a very simple measure of complexity, is able to capture variations both in the driving terms and in the output, along the solar cycle. These results are consistent with analogous studies of fractality for geomagnetic indexes such as Dst or SYM-H.