Coherent structures in screened two-dimensional turbulence

Abstract

Using a collection of vortex patches as fundamental objects of interest, two-dimensional (2D) coherent structure solutions are constructed as extremum entropy states (long time states) for a system of interacting screened 2D vortices. For a typical initial condition considered, such as a thin film of generalized vorticity in a semi-periodic domain, the phase diagram is numerically obtained for a wide range of total energy values. The inverse cascade phenomenon (the formation of a large scale structure from small scales) is demonstrated by computing the entropies for various length scales at a fixed energy value. Finally, a Monte Carlo simulation of vortex patches is performed and it is found that except for very large energies, the simulation results agree well with the equilibrium calculations.