  We apply the concept of helicity from classical hydrodynamics to elucidate
two problematical issues in cosmic string physics. Helicity, the space integral
of the scalar product of a velocity-like field with its vorticity field (curl),
can be defined for a complex scalar field in analogy with fluids. We dwell on
the topological interpretation of helicity as related to the linking of field
lines of the vorticity field. Earlier works failed to fully implement this
interpretation for cosmic strings by missing a term connected with the linking
of these lines inside the strings. As a result paradoxical conclusions were
drawn: global cosmic string loops may not take on certain simple shapes, and
baryon number is not quantized in integers in the presence of local cosmic
strings in gauge theory. We show that both paradoxes are removed when internal
contributions to helicity are properly taken into account. In particular,
quantization of baryon number can be understood within a special case of the
Glashow-Weinberg-Salam model if cosmic strings are the unique mechanism for
baryosynthesis. In addition, we find a new constraint on the permitted linkages
of cosmic strings in a string tangle.
