  Helicity is a fundamental property of magnetic fields, conserved in ideal
MHD. In flux rope topology, it consists of twist and writhe helicity. Despite
the common occurrence of helical structures in the solar atmosphere, little is
known about how their shape relates to the writhe, which fraction of helicity
is contained in writhe, and how much helicity is exchanged between twist and
writhe when they erupt. Here we perform a quantitative investigation of these
questions relevant for coronal flux ropes. The decomposition of the writhe of a
curve into local and nonlocal components greatly facilitates its computation.
We use it to study the relation between writhe and projected S shape of helical
curves and to measure writhe and twist in numerical simulations of flux rope
instabilities. The results are discussed with regard to filament eruptions and
coronal mass ejections (CMEs). We conclude that the writhe is useful in
interpreting S shaped coronal structures and in constraining models of
eruptions.
