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We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of the 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 being zero there.
Lyons, T. Particle trajectories in extreme Stokes waves over inifinte depth. Discrete and Continuous Dynamical Systems A: 34-8 August 2014 issue. DCDS-A 34-8 August 2014 issue