Recent progress on particle trajectories in steady water waves
Mats Ehrnström - Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany (email)
Abstract: We survey recent results on particle trajectories within steady two-dimensional water waves. Particular emphasis is placed on the linear and exact mathematical theory of periodic and symmetric waves, and the effects of a (possibly rotational) background current. The different results vindicate and detail the classical Stokes drift, and also show the transition of orbits when waves propagate into running water. The classical approximation, depicting the trajectories as closed ellipses, is shown to be a mathematical rarity.
Keywords: Steady water
waves; Stokes waves, Particle trajectories, Vorticity, Background
Received: March 2009; Revised: June 2009; Available Online: July 2009.
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