Nonlocal vorticity cascade in two dimensions

Abstract

The whole set of simultaneous correlation functions describing steady vorticity cascade is obtained from the Euler equation by a straightforward procedure. Nonlocality of the cascade provides for a large logarithmic parameter that enables one to obtain a universal set of the correlation functions of the vorticity ω in the inertial interval: 〈${\mathrm{\omega }}^{\mathit{n}}$(${\mathbf{r}}_1$)${\mathrm{\omega }}^{\mathit{n}}$(${\mathbf{r}}_2$)〉∝${\ln }^{2\mathit{n}/3\mathrm{}}$(L/‖${\mathbf{r}}_1$ -${\mathbf{r}}_2$‖), with L being the scale of the external pump.