Scatter-plots of the total flux-tube expansion rate as a function of the magnetic field strength at the surface. The top panel represent these quantities calculated from our simulations for an 11 yr period. The points are colour-coded according to the speed attained by the wind flow in each flux-tube (orange represents fast wind, blue represents slow wind). The bottom panel represents only the simulation data points relative to the minimum and to the maximum (first and third panels in Fig. 5).