Equilibrium states of finite-dimensional approximations of a two-dimensional incompressible inviscid fluid

Equilibrium states of Arakawa approximations of a two-dimensional incompressible inviscid fluid are investigated in the case of high resolution $8192^2$. Comparison of these states with quasiequilibrium states of a viscid fluid is made. Special attention is paid to the stepped shape of large coherent structures and to the presence of small vortices in final states. It is shown that the large-scale dynamics of Arakawa approximations are similar to the theoretical predictions for an ideal fluid. Cesaro convergence is investigated as an alternative technique to get condensed states. Additionally, it can be used to solve the problem of nonstationary final states.