Received xx; revised xx; accepted xx)We want to study the connections between the magnetic field generated inside the Sun and the solar wind impacting Earth, especially the influence of north-south asymmetry on the magnetic and velocity fields. We study a solar-like 11-year cycle in a quasi-static way : an asymmetric dynamo field is generated through a 2.5D flux-transport model with Babcock-Leighton mechanism, and then is used as bottom boundary condition for compressible 2.5D simulations of the solar wind. We recover solar values for the mass loss rate, the spin-down timescale and the Alfvén radius, and are able to reproduce the observed delay in latitudinal variations of the wind and the general wind structure observed for the Sun. We show that the phase-lag between the energy of the dipole component and the total surface magnetic energy has a strong influence on the amplitude of the variations of global quantities. We show in particular that the magnetic torque variations can be linked to topological variations during a magnetic cycle, while variations in the mass loss rate appeared to be driven by variations of the magnetic energy.