Universal Velocity Profile for Coherent Vortices in Two-Dimensional Turbulence

TL;DR

This paper develops a rigorous theory explaining the universal velocity decay profile within coherent vortices in two-dimensional turbulence, characterized by an $rac{1}{4}$ power-law scaling, independent of small-scale turbulence details.

Contribution

The paper introduces a universal theoretical framework for the velocity profile in 2D turbulence vortices, confirming the $rac{1}{4}$ scaling law through analysis.

Findings

The velocity profile follows a $r^{-1/4}$ scaling law.

The scaling law is universal, unaffected by small-scale turbulence injection.

The theory aligns with previous numerical and laboratory observations.

Abstract

Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with small-scale fluctuations. We present a rigorous theory explaining the $\eta=1/4$ scaling in the $V\propto r^{-\eta}$ law of the velocity spatial profile within a vortex, where $r$ is the distance from the vortex center. This scaling, consistent with earlier numerical and laboratory measurements, is universal in its independence of details of the small-scale injection of turbulent fluctuations and details of the shape of the box.