Particle trajectories in extreme Stokes waves over infinite depth
Tony Lyons
Discrete & Continuous Dynamical Systems - A 2014, 34(8): 3095-3107 doi: 10.3934/dcds.2014.34.3095
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.
keywords: weak solution maximum principles particle trajectory. Stokes wave
The 2-component dispersionless Burgers equation arising in the modelling of blood flow
Tony Lyons
Communications on Pure & Applied Analysis 2012, 11(4): 1563-1576 doi: 10.3934/cpaa.2012.11.1563
This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well as applications of the model to clinical conditions.
keywords: breaking waves dispersionless limit. Blood flow nonlinear waves

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