Anisotropic characteristics of the kraichnan direct cascade in two-dimensional hydrodynamic turbulence

The 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 = C _Kη^2/3k^–3, where η is the enstrophy flux and the Kraichnan constant C _K ? 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function S ₃ ^L which, as for the isotropic turbulence, gives the same scaling with respect to the separation length R and η, S ₃ ^L = C ₃ηR ³, but the average over the angles and time differs from its isotropic value.