Horizontal transport in the stratosphere is dominated by the large-scale velocity field: breaking planetary waves give rise to a large-scale "stirring", which is a form of chaotic advection. In the mesosphere, there is a significant unbalanced component to the flow due to the strongly enhanced presence of high-frequency gravity waves. We seek an understanding of the manner in which the unbalanced component influences the velocity field and its gradients, and the implications for mixing. The concepts of balance versus imbalance and spectral nonlocality versus locality are used to analyse results from two shallow-water numerical experiments representative of stratospheric and mesospheric dynamics on a quasi-horizontal isentropic surface. Geometrical diagnostics demonstrate that velocity gradients are strongly influenced by the unbalanced component of the flow. This behaviour is further confirmed in statistical analyses of absolute (single-particle) and relative (two-particle) dispersion. In particular, spectrally nonlocal and local dynamics are reflected in the distinctive behaviour evident in the relative dispersion statistics found for the stratospheric and mesospheric experiments. Results from such geometrical and statistical analyses suggest that horizontal transport in the mesosphere may be modelled as a diffusive process.