Relative dispersion in direct cascades of generalized two-dimensional turbulence

The statistical features of turbulent flows depend on the locality properties of energy transfers among scales. The latter, in turn, may have consequences for the relative dispersion of passive particles. We consider a class of two-dimensional flows of geophysical interest, namely α-turbulence models, possessing different locality properties. We numerically study relative dispersion in such flows using both fixed-time and fixed-scale indicators. The results are compared with predictions based on phenomenological arguments to explore the relation between the locality of the turbulent cascade and that of relative dispersion. We find that dispersion behaviors agree with expectations from local theories, for small enough values of the parameter α (dynamics close to surface quasi geostrophy) and for sufficiently small initial pair separations. Non-local dispersion is instead observed for the largest α considered (quasi-geostrophic model).