Geometric Aspects of Spatially Periodic Interfacial Waves

Periodic waves at the interface between two inviscid fluids of differing densities are considered from a geometric point of view. A new Hamiltonian formulation is used in the analysis and restriction of the Hamiltonian structure to space‐periodic functions leads to an O ‐invariant Hamiltonian system. Motivated by the simplest O ‐invariant Hamiltonian system, the spherical pendulum, we analyze the properties of traveling waves, standing waves, interactions between standing and traveling waves (mixed waves) and time‐modulated spatially periodic waves. A singularity in the bifurcation of traveling waves leads to a nonlinear resonance and this is investigated numerically.