  We study spreading wave packets in a disordered nonlinear ladder with broken
time-reversal symmetry induced by synthetic gauge fields. The model describes
the dynamics of interacting bosons in a disordered and driven optical ladder
within a mean-field approximation. The second moment of the wave packet $m_{2}
= g t^{\alpha}$ grows subdiffusively with the universal exponent $\alpha \simeq
1/3$ similar to the time-reversal case. However the prefactor $g$ is strongly
modified by the field strength and shows a non-monotonic dependence. For a weak
field, the prefactor increases since time-reversal enhanced backscattering is
suppressed. For strong fields the spectrum of the linear wave equation reduces
the localization length through the formation of gaps and narrow bands.
Consequently the prefactor for the subdiffusive spreading law is suppressed.
