Two-Dimensional Interactions in a Field of Vortices

A key aspect of decaying two-dimensional turbulence is the presence of coherent vortex structures. These vortices undergo mutual advection and participate in strong inelastic interactions which transfer energy and enstrophy across spatial scales thereby influencing the inverse and direct cascades. The coupled behavior of coherent structures and cascade processes depends on the various interactions occurring in the flow. While much has been learned from studies of isolated vortex pairs, and in particular symmetric merger, other interactions and outcomes are possible in a field of varying vortices. A more generalized characterization of interactions and their statistics is needed to better understand two-dimensional turbulent flows.

Here we perform DNS of a two-dimensional incompressible viscous model flow initially consisting of an array of unequal vortices. Various interaction types are directly assessed and categorized based on their underlying physics and influence on the flow evolution. Initial conditions are varied to understand how the population of vortices relate to the types of interactions that occur. This work is a step towards a statistical characterization of vortex interactions required to link coherent structures to cascades processes.