Statistical properties of freely decaying two-dimensional hydrodynamic turbulence

Statistical characteristics of freely decaying two-dimensional hydrodynamic turbulence at high Reynolds numbers are numerically studied. In particular, numerical experiments (with resolution up to $8192\times 8192$) provide a Kraichnan-type turbulence spectrum $E_k\sim k^{-3}$. By means of spatial filtration, it is found that the main contribution to the spectrum comes from sharp vorticity gradients in the form of quasi-shocks. Such quasi-singularities are responsible for a strong angular dependence of the spectrum owing to well-localized (in terms of the angle) jets with minor and/or large overlapping. In each jet, the spectrum decreases as $k^{-3}$. The behavior of the third-order structure function accurately agrees with the Kraichnan direct cascade concept corresponding to a constant enstrophy flux. It is shown that the power law exponents $\zeta_n$ for higher structure functions grow with n more slowly than the linear dependence, thus indicating turbulence intermittency.