1202.5001 (Delia Ionescu-Kruse)

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

Delia Ionescu-Kruse

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.

View original: http://arxiv.org/abs/1202.5001