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Effects of the second vertical mode and nonlinearity of the background flow field on the Lagrangian transport of particle clouds are studied by employing a wind-forced linear hydrostatic model and a weakly-nonlinear, weakly-nonhydrostatic evolution model. It is confirmed that Kelvin waves primarily advect particles near the basin perimeter in a cyclonic direction, and Poincaré waves primarily advect particles in off-shore (radial) directions in a manner that is oscillatory in time with frequencies near the inertial period. The internal current associated with the second vertical mode is usually far smaller than that associated with the energetically dominant, lowest vertical mode. However, because of the disparately slow eigenspeed of the vertical mode-two Kelvin wave, the resultant particle transport associated with the vertical mode-two flow near the basin perimeter can drive transport that is comparable with that associated with the Kelvin wave of the lowest vertical mode. It is discovered that nonlinear interaction between the Kelvin-Poincaré wave pair can give birth to a solitary-like wave of large amplitude in an off-shore region. This new type of wave generates a large current and co-propagates with the Kelvin wave in a cyclonic direction and, eventually, can cause a burst of particle transport in an off-shore direction

Lagrangian transport in a circular lake: effect of nonlinearity and the second vertical mode