Elliptic and hyperelliptic functions describing the particle motion beneath small-amplitude water waves with constant vorticity
Mathematical Physics
2011-08-25 v2 math.MP
Abstract
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed curves. Some solutions can be expressed in terms of Jacobi elliptic functions, others in terms of hyperelliptic functions. We obtain new kinds of particle paths. We make some remarks on the stagnation points which could appear in the fluid due to the vorticity.
Keywords
Cite
@article{arxiv.1106.3824,
title = {Elliptic and hyperelliptic functions describing the particle motion beneath small-amplitude water waves with constant vorticity},
author = {Delia Ionescu-Kruse},
journal= {arXiv preprint arXiv:1106.3824},
year = {2011}
}
Comments
Discrete and Continuous Dynamical Systems - Series B 2011