Establishing a physical mechanism behind the inverse cascade in two-dimensional turbulence: vortex mergers in the presence of background shear

The inverse energy cascade, which causes energy to accumulate at large scales, is a unique and characteristic feature of two-dimensional turbulence. Despite a long history of systematic study, the underlying physical mechanism behind the cascade is still not well understood. One ubiquitous physical process that mediates the transfer of energy from small to large scales is vortex mergers. Previous work focused mainly on the interaction of pairs of isolated co-rotating vortices immersed in an irrotational background flow. In this talk, we extend this work to a configuration more relevant to turbulence, where small-scale vortices are immersed in a large-scale background flow with shear. We find that whether the vortices merge or scatter is determined by a pair of nondimensional parameters, analogous to the ratio of small- and large-scale vorticity and the ratio of the separation distance to vortex size.