Velocity statistics inside coherent vortices generated by the inverse cascade of $2d$ turbulence

TL;DR

This paper investigates velocity fluctuations within coherent vortices in 2D turbulence, revealing non-trivial scaling and anisotropy in the structure functions, advancing understanding of turbulence dynamics.

Contribution

It provides new calculations of velocity fluctuation correlations, demonstrating non-trivial scaling and anisotropy within vortices generated by the inverse cascade.

Findings

Non-trivial scaling of the structure function

Strong anisotropy of the structure function

Universal velocity profile corresponds to passive flow fluctuations

Abstract

We analyze velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \cite{16KL}, the universal velocity profile, established in \cite{14LBFKL}, corresponds to the passive regime of flow fluctuations. The property enables one to calculate correlation functions of the velocity fluctuations in the universal region. We present results of the calculations that demonstrate a non-trivial scaling of the structure function. In addition the calculations reveal strong anisotropy of the structure function.