There exist analytic solutions to the fold and twist flow that indicate the
occurence of a topological phase transition. This flow is a modification of the
saddle node Hopf bifurcation, and is related to "torsion" (vortex) bursting.
This work was done about 1990. Bayer and Moffett used computer methods to
describe the flow, but analytic closed form solutions exist and were discovered
by using Cartan methods in rotating frames of reference.