  This work revisits the production of vorticity at an interface separating two
immiscible incompressible fluids. A new decomposition of the vorticity flux is
proposed in a two-dimensional context which allows to compute explicitly such a
quantity in terms of surface tension $\sigma$, viscosity $\mu$ and gravity $g$.
This approach is then applied in the context of gravito-capillary waves. It
leads to analytical results already known but from a new perspective, provides
some quantitative predictions at short time that can be a good test for
numerical codes. Finally it is a mean to obtain a qualitative understanding of
direct numerical simulation results.
