Traveling water waves on a sphere Original Research Article

We study numerically a model of weakly non-linear water waves on the surface of a layer surrounding a gravitating sphere. The equations of motion are non-local and Hamiltonian and our numerical implementation preserves these structures. We focus on a class of traveling and standing waves that are “near-monochromatic” in space, i.e. waves whose amplitude consists of one spherical harmonic plus small corrections. We observe that such motions are stable for long time, and we use methods from Hamiltonian dynamical systems to understand the numerical observations theoretically.