The solar wind speed at 1 AU shows variations in latitude and in time which
reflect the evolution of the global background magnetic field during the
activity cycle. It is commonly accepted that the terminal wind speed in a
magnetic flux-tube is anti-correlated with its expansion ratio, which motivated
the definition of widely-used semi-empirical scaling laws relating one to the
other. In practice, such scaling laws require ad-hoc corrections. A predictive
law based solely on physical principles is still missing. We test whether the
flux-tube expansion is the controlling factor of the wind speed at all phases
of the cycle and at all latitudes using a very large sample of wind-carrying
open magnetic flux-tubes. We furthermore search for additional physical
parameters based on the geometry of the coronal magnetic field which have an
influence on the terminal wind flow speed. We use MHD simulations of the corona
and wind coupled to a dynamo model to provide a large statistical ensemble of
open flux-tubes which we analyse conjointly in order to identify relations of
dependence between the wind speed and geometrical parameters of the flux-tubes
which are valid globally (for all latitudes and moments of the cycle). Our
study confirms that the terminal speed of the solar wind depends very strongly
on the geometry of the open magnetic flux-tubes through which it flows. The
total flux-tube expansion is more clearly anti-correlated with the wind speed
for fast rather than for slow wind flows, and effectively controls the
locations of these flows during solar minima. Overall, the actual asymptotic
wind speeds attained are also strongly dependent on field-line inclination and
magnetic field amplitude at the foot-points. We suggest ways of including these
parameters on future predictive scaling-laws for the solar wind speed.Comment: Accepted for publicaton on Astronomy & Astrophysic