A simple model of two-dimensional (depth averaged) flow in topographic gyres by wind action on a shallow model lake is shown to produce chaotic particle motions in the case where the wind alternately blows from two prescribed directions. The nature of the motions of the advected particles is of the generic type known from Hamiltonian systems: islands of regular motion surround elliptic periodic points and chaotic regions are related to hyperbolic periodic points. The effect of vertical-shear dispersion is simulated by adding random displacements to the advective particle displacements. The contributions of chaotic advection and shear dispersion to the growth of the mean distance between particles are examined in some detail.