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We study two-dimensional periodic capillary-gravity water waves propagatingat the free surface of water in a flow with arbitrary, prescribed vorticityover a flat bed. Using conformal mappings and a new Babenko-type reformulationof Bernoulli's equation, the problem is equivalently cast into the form"identity plus compact", which is amenable to Rabinowitz' global bifurcationtheorem, while no restrictions on the geometry of the surface profile and noassumptions regarding the absence of stagnation points in the flow have to bemade. Within the scope of this new formulation, local and global solutioncurves, bifurcating from laminar flows with a flat surface, are constructed.

Global bifurcation of capillary-gravity water waves with overhanging profiles and arbitrary vorticity