Statistical features of freely decaying two-dimensional hydrodynamic turbulence

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 $8192\times 8192$) provide a Kraichnan-type turbulence spectrum $E_k\sim k^{-3}$. 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 ${\zeta }_n$ for higher structure functions grow more slowly than the linear dependence of $n$, which testifies to turbulence intermittency.

7 pages, 10 figures

Cited by in corpus (6)

• Development of high vorticity structures in incompressible 3D Euler equations
• Development of high vorticity structures and geometrical properties of the vortex line representation
• Anisotropic characteristics of the Kraichnan direct cascade in two-dimensional hydrodynamic turbulence
• Compressible vortex structures and their role in the onset of hydrodynamic turbulence
• Isotropization of two-dimensional hydrodynamic turbulence in the direct cascade
• Statistical properties of the velocity field for the 3D hydrodynamic turbulence onset