No abstract

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 the 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 Kraichnan direct cascade concept corresponding to a constant enstrophy flux. It is shown that the power law exponents ζn for higher structure functions grow more slowly than the linear dependence of n, which testifies to turbulence intermittency.

Statistical characteristics of the Kraichnan direct cascade for two-dimensional hydrodynamic turbulence are numerically studied (with spatial resolution 8192×8192) in the presence of pumping and viscous-like damping. It is shown that quasi-shocks of vorticity and their Fourier partnerships in the form of jets introduce an essential influence in turbulence leading to strong angular dependencies for correlation functions. The energy distribution as a function of modulus k for each angle in the inertial interval has the Kraichnan behavior, ∼ k −4 , and simultaneously a strong dependence on angles. However, angle average provides with a high accuracy the Kraichnan turbulence spectrum E k = CKη 2/3 k −3 where η is enstrophy flux and the Kraichnan constant CK ≃ 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function S L 3 which, as for the isotropic turbulence, gives the same scaling with respect to separation length R and η, S L 3 = C3ηR 3 , but the mean over angles and timeC3 differs from its isotropic value.