Internal doubly periodic gravity-capillary waves with vorticity (Q6642441)

The author considers a system of multiple layers of immiscible fluids of separated by free interfaces. Each fluid satisfies the homogeneous incompressible Euler equation with a vertical gravity force, and non-trivial interfacial tension determines density jumps at each interface.\N\NIt is proved, for a subset of the parameter space, the existence of a continuous family of small-amplitude spatially (doubly) periodic travelling wave solutions that are strong Beltrami fields in the sense that the vorticity is parallel to the velocity with a constant proportionality factor.\N\NThe proof relies on a general multiparameter bifurcation result (extending the Crandall-Rabinowitz bifurcation theorem) that is stated and proved in the Appendix.