  We investigate particle trajectories in equatorial flows with geophysical
corrections caused by the earth's rotation. Particle trajectories in the flows
are constructed using pairs of analytic functions defined over the labelling
space used in the Lagrangian formalism. Several classes of flow are
investigated, and the physical regime in which each is valid is determined
using the pressure distribution function of the flow, while the vorticity
distribution of each flow is also calculated and found to be effected by
earth's rotation.
