Particle trajectories in extreme Stokes waves over infinite depth

Tony Lyons

doi:10.3934/dcds.2014.34.3095

Article Contents

2014, Volume 34, Issue 8: 3095-3107. Doi: 10.3934/dcds.2014.34.3095

This issue Previous Article On the nature of large and rogue waves Next Article Dispersion relations for periodic water waves with surface tension and discontinuous vorticity

Particle trajectories in extreme Stokes waves over infinite depth

Tony Lyons^1,

1.
School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8

Received: July 2013

Revised: September 2013

Published: August 2014

Abstract / Introduction Related Papers Cited by

Abstract

We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid particles being zero there.

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Mathematics Subject Classification: 76B15, 35B50, 35Q35.

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