  A boson two--leg ladder in the presence of a synthetic magnetic flux is
investigated by means of bosonization techniques and Density Matrix
Renormalization Group (DMRG). We follow the quantum phase transition from the
commensurate Meissner to the incommensurate vortex phase with increasing flux
at different fillings. When the applied flux is $\rho \pi$ and close to it,
where $\rho$ is the filling per rung, we find a second incommensuration in the
vortex state that affects physical observables such as the momentum
distribution, the rung-rung correlation function and the spin-spin and
charge-charge static structure factors.
