Statistical properties of freely decaying two-dimensional hydrodynamic turbulence
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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 × 8192) provide a Kraichnan-type turbulence spectrum E k ∼ 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 ξ n for higher structure functions grow with n more slowly than the linear dependence, thus indicating turbulence intermittency.
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