# American Institute of Mathematical Sciences

August  2014, 34(8): 3095-3107. doi: 10.3934/dcds.2014.34.3095

## Particle trajectories in extreme Stokes waves over infinite depth

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

Received  July 2013 Revised  September 2013 Published  January 2014

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.
Citation: Tony Lyons. Particle trajectories in extreme Stokes waves over infinite depth. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3095-3107. doi: 10.3934/dcds.2014.34.3095
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