Particle paths in small amplitude solitary waves with negative vorticity
  We investigate the particle trajectories in solitary waves with vorticity, where the vorticity is assumed to be negative and decrease with depth. We show that the individual particle moves in a similar way as that in the irrotational case if the underlying laminar flow is favorable, that is, the flow is moving in the same direction as the wave propagation throughout the fluid, and show that if the underlying current is not favorable, some particles in a sufficiently small solitary wave move to the opposite direction of wave propagation along a path with a single loop or hump . 
Ling-Jun Wang
math.AP