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This work addresses two problems: 1) the dispersion induced by a cloud of vortices near a straight coast-line when the bottom is flat and the coastal boundary is a vertical plane or when the bottom is a planar slope; 2) the dynamics of vortices moving over a planar sloping bottom. Vortices near a vertical boundary are studied by the well-known method of images. For a plane sloping bottom we describe and develop a model, first introduced by Peregrine (1996) that uses a sector of a vortex ring to model a vortex in a wedge of fluid, where the wedge is formed by the water surface and by the planar sloping bottom. Numerical simulations using these free-slip analytical models are used to investigate the dispersion of vorticity and of a passive tracer induced by clouds of vortices. The results of the two models are compared. The dispersion of vortices and particles is mainly affected by the formation of vortex dipoles. The shoreline sets a preferential direction for the dispersion process and the dispersion normal to the shoreline is generally smaller, or bounded when the vortices forming the dipole have different absolute circulation. The dispersion of particles is generally smaller than the dispersion of vortices. In the second part of this work the analytical model of Peregrine (1996) for vortices moving over a planar slope at an angle a with the horizontal is tested against a set of laboratory experiments. Experiments were made by studying the dynamics of a vortex dipole moving towards a planar sloping beach. We measured the minimum distance from the shoreline reached by the vortices and their along-shore speed. The parameter ranges examined were 3~ 1500.