  Observations of solar flare ribbons show significant fine structure in the
form of breaking wave-like perturbations and spirals. The origin of this
structure is not well understood, but one possibility is that it is related to
the tearing instability in the flare current sheet. Here we study this
connection by constructing an analytical three-dimensional magnetic field
representative of an erupting flux rope with a flare current sheet below it. We
introduce small-scale flux ropes representative of those formed during a
tearing instability in the current layer, and use the squashing factor on the
solar surface to identify the shape of the presumed flare ribbons and fine
structure. Our analysis suggests there is a direct link between flare-ribbon
fine structure and flare current sheet tearing, with the majority of the ribbon
fine structure related to oblique tearing modes. Depending upon the size,
location and twist of the small-scale flux ropes, breaking wave-like and spiral
features within the hooks and straight sections of the flare ribbon can be
formed that are qualitatively similar to observations. We also show that the
handedness of the spirals/waves must be the same as the handedness of the hooks
of the main ribbon. We conclude that tearing in the flare current layer is a
likely explanation for spirals and wave-like features in flare ribbons.
