Interaction of turbulence and large-scale vortices in incompressible 2D fluids

It is commonplace in 2D fluid dynamics that intense large-scale vortices arise during turbulence decay. Both the large-scale vortex and the turbulent components will be important in the further evolution: the vortices will modify the turbulent dynamics and, in turn, will be modified by the turbulence. Using Wigner functions, we derive a new two-component model to describe interaction of turbulence and intense large-scale vortices in incompressible inviscid 2D fluids. We apply this model to study the dynamics of a vortex dipole propagating through turbulence, a problem that allows an elegant analytic solution.