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VOLUME 102 (2015) | ISSUE 11 | PAGE 870
Anisotropic characteristics of the Kraichnan direct cascade in two-dimensional hydrodynamic turbulence
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, {\sim} k^{-4}, and simultaneously a strong dependence on angles. However, angle average provides with a high accuracy the Kraichnan turbulence spectrum Ek=CKη2/3 k-3, where η is enstrophy flux and the Kraichnan constant C_{\text{K}}\simeq 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function S3L which, as for the isotropic turbulence, gives the same scaling with respect to separation length R and η, S3L=C3η R3, but the mean over angles and time \bar {C_3} differs from its isotropic value.