Anisotropic characteristics of the kraichnan direct cascade in two-dimensional hydrodynamic turbulence
Abstract
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 3η R 3, but the average over the angles and time differs from its isotropic value.
- Publication:
-
Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- December 2015
- DOI:
- 10.1134/S0021364015230083
- arXiv:
- arXiv:1510.09052
- Bibcode:
- 2015JETPL.102..760K
- Keywords:
-
- Physics - Fluid Dynamics;
- Condensed Matter - Statistical Mechanics;
- Nonlinear Sciences - Chaotic Dynamics;
- Physics - Computational Physics
- E-Print:
- 6 pages, 7 figures