Elliptic and hyperelliptic functions describing the particle motion beneath small-amplitude water waves with constant vorticity

2011/06/20 by Delia Ionescu-Kruse, Ionescu-Kruse, Delia · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1106.3824

Discrete and Continuous Dynamical Systems - Series B 2011

arxiv created 2011/08/24 · arxiv updated 2011/08/25

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.

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