Effects of geometry on the flux of vorticity from a free surface are discussed. Special attention is paid to situations where curvature-dependent contributions to the vorticity flux can be neglected. The geometry of vortex lines embedded in the surface is discussed in this context. These results show that vortex lines can be straight and geometry-induced vorticity flux is produced; conversely vortex lines can be curved and no geometry-induced vorticity flux is produced. A convenient method for assessing vorticity flux from a steady surface based on Gaussian curvature is derived.

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