The transport of scalars in the coastal ocean is considered through the analysis of a vertically constrained plume which disperses laterally. Observations of the plume are made using an autonomous underwater vehicle (AUV) operating in two modes: (i) repeated transects of the plume at a fixed distance from the source; and (ii) a large-scale mapping of the plume development. Together, these measurements define both the variability in the plume centreline (i.e. the meandering) and the growth of the plume around the centreline (i.e. the relative dispersion). The analysis of the measurements suggests that the meandering is well-described by a spatially uniform but temporally variable velocity field, indicating that large-scale flow structures dominate the centreline variability. The growth of the plume downstream is seen to follow a scale-dependent dispersion law, most likely of a compound structure: a 4/3-law in the near field, and a scale-squared law in the far field. This transition between dispersion laws is consistent with the transition from three-dimensional turbulence structures to two-dimensional eddies, which is due to the constraints imposed on the vertical dimension at the site. Comparing the two dispersion processes, the effective dispersion created by meandering is found to be comparable with or larger than the relative dispersion in the near field; but in the far field, the relative dispersion is found to dominate considerations of overall dispersion.