  Analytic global bifurcation theory is used to construct a large variety of
families of steady periodic two-dimensional gravity water waves with
real-analytic vorticity distributions, propagating in an incompressible fluid.
The waves that are constructed can possess an arbitrary number of interior
stagnation points in the fluid, and corresponding critical layers consisting of
closed streamlines. This is made possible by the use of the so-called naive
flattening transform, which has previously only been used for local
bifurcation.
