  We compute the spectrum of gluons emitted by a highly energetic quark inside
a flowing QCD medium, focusing on the soft gluon limit at first order in the
opacity expansion. Specifically, we derive the leading energy-suppressed
corrections to the double differential final parton distribution, and show that
they are substantial for both static and flowing matter. In particular, we
demonstrate that the corrections due to the transverse flow become large even
at moderate energies and flow velocities, affecting drastically both the shape
and magnitude of the spectrum. We observe that the final transverse momentum of
the emitted gluon tends to align along the flow direction, resulting in a
non-trivial azimuthal distribution. These results can be directly implemented
into the estimation of multiple observables to get a better understanding of
the jet-medium interaction processes in HICs.
