Self-similar coherent structures in two-dimensional decaying turbulence

The authors present a detailed study of the emergence and the long-time behaviour of coherent vortices in two-dimensional decaying turbulence. By high-resolution numerical experiments they find that the coherent structures are self-similar, i.e. their energy, enstrophy and size satisfy scaling laws. Moreover, the knowledge of the statistical distribution of the size of these vortices is sufficient to compute the energy spectrum of the 2D turbulent flow and to explain the significant deviations from the Kraichnan-Batchelor theory. At long times the motion of the fluid is dominated by the vortex dynamics, which is strikingly similar to the Hamiltonian motion of few point vortices, as is confirmed by a comparison between the numerical simulations of the two systems.