On the particle paths and the stagnation points in small-amplitude deep-water waves

Abstract

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.

to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with arXiv:1106.3824

References in corpus (4)

• Steady periodic water waves with constant vorticity: regularity and local bifurcation
• Particle trajectories in linearized irrotational shallow water flows
• Peakons arising as particle paths beneath small-amplitude water waves
• On particle trajectories in linear deep-water waves