JETP Letters

, Volume 102, Issue 11, pp 760–765 | Cite as

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

  • E. A. Kuznetsov
  • E. V. Sereshchenko
Nonlinear Phenomena


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 Kη2/3k–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.


Vorticity JETP Letter Isotropic Turbulence Inertial Range Spectral Space 
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Copyright information

© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  4. 4.Khristianovich Institute of Theoretical and Applied Mechanics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  5. 5.Far-Eastern Federal UniversityVladivostokRussia

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