Evolution of the vorticity-area density during the formation of coherent structures in two-dimensional flows

It is shown: (1) that in two-dimensional, incompressible, viscous flows the vorticity-area distribution evolves according to an advection-diffusion equation with a negative, time dependent diffusion coefficient and (2) how to use the vorticity-stream function relations, i.e., the so-called scatter-plots, of the quasi-stationary coherent structures in order to quantify the experimentally observed changes of the vorticity distribution moments leading to the formation of these structures.