Study of the fractality in an MHD Shell model forced by solar wind fluctuations

Abstract

Abstract. The description of the relationship between interplanetary plasma and geomagnetic activity requires complex models. Drastically reducing the ambition of describing this detailed complex interaction, and if we are interested only in the fractality properties of the time-series of its characteristic parameters, a magnetohydrodynamic (MHD) shell model forced using solar wind data, might provide a possible novel approach. In this paper we study the relation between the activity of the magnetic energy dissipation rate obtained in one such model, which may describe geomagnetic activity, and the fractal dimension of the forcing. In different shell model simulations, the forcing is provided by the solution of a Langevin equation where a white noise is implemented. Since this forcing has shown its unsuitableness in describing the driver due to solar wind action, we propose to consider the fluctuations of the product between the velocity and the magnetic field solar wind data as the noise in Langevin equation, whose solution provides the forcing in the magnetic field equation. We compare the fractal dimension of the magnetic energy dissipation rate obtained, of the magnetic forcing term, and of the fluctuations of v · bz, with the activity of the magnetic energy dissipation rate. We examine the dependence of these fractal dimensions on the solar cycle. We show that all measures of activity have a peak near solar maximum. Moreover, both the fractal dimension computed for the fluctuations of v · bz time series and the fractal dimension of the magnetic forcing have a minimum near solar maximum. This suggests that the complexity of the noise term in the Langevin equation may have a strong effect in the activity of the magnetic energy dissipation rate.