  Cosmic string networks form during cosmological phase transitions as a
consequence of the Kibble mechanism. The evolution of the simplest networks is
accurately described by the canonical Velocity Dependent One-Scale (VOS) model.
However, numerical simulations have demonstrated the existence of significant
quantities of short-wavelength propagation modes on the strings, known as
wiggles, which motivated the recent development of a wiggly string extension of
the VOS. Here we summarize recent progress in the physical interpretation of
this model through a systematic study of the allowed asymptotic scaling
solutions of the model. The modeling mainly relies on three mechanisms: the
universe's expansion rate, energy transfer mechanisms (e.g., the production of
loops and wiggles), and the choice of the scale in which wiggles are
coarse-grained. We consider the various limits in which each mechanism
dominates and compare the scaling solutions for each case, in order to gain
insight into the role of each mechanism in the overall behavior of the network.
Our results show that there are three scaling regimes for the wiggliness,
consisting of the well-known Nambu-Goto solution, and non-trivial regimes where
the amount of wiggliness can grow as the network evolves or, for specific
expansion rates, become a constant. We also demonstrate that full scaling of
the network is more likely in the matter era than in the radiation epoch, in
agreement with numerical simulations.
