Relative Dispersion in QG and SQG Turbulence

Statistical properties of turbulent fluids depend on how local are the energy transfers among scales, i.e. whether the energy transfer at some given scale is due to the eddies at that particular scale, or it is due to eddies at larger (nonlocal) scale. This locality in the energy transfers may have consequences on the relative dispersion of passive particles. Two quasigeostrophic models are well known that may represent either nonlocal scale interactions or local scale interactions: the standard barotropic (QG) model and the surface quasi-geostrophic (SQG) model.

We examine the relative dispersion statistics for each class of model, both as a function of time and as a function of scale, and compare to predictions based on phenomenological arguments. We find that dispersion statistics in the SQG case follow the predicted values from local theory for initially small enough separations. In contrast, nonlocal dispersion is observed for the QG model. However, we point out that spectral energy transfers do have a nonlocal contribution in the SQG case which indicates that locality/nonlocality of the turbulent cascade may not always imply locality/nonlocality in the relative dispersion of particles. It is found that the kinetic spectral slope has some importance for shaping the self-similarity scalings that are important to determine the localness of the dispersion.