Lack of self-similarity in transverse velocity increments and circulation statistics in two-dimensional turbulence

TL;DR

This paper investigates the statistical properties of velocity increments and circulation in 2D turbulence, revealing anomalous scaling in transverse structure functions and establishing a relation between circulation and transverse increments.

Contribution

It demonstrates the lack of self-similarity in transverse velocity increments and derives an analytical relation linking circulation scaling exponents to transverse structure functions.

Findings

Transverse structure functions show anomalous scaling.

Longitudinal structure functions exhibit self-similarity.

A theoretical relation connects circulation exponents to transverse increments.

Abstract

We study the statistics of longitudinal and transverse structure functions, as well as velocity circulation in the inverse energy cascade of two-dimensional turbulence. By means of direct numerical simulations of the incompressible Navier-Stokes equations, we show that transverse structure functions exhibit an anomalous scaling, in contrast to the self-similar behavior of longitudinal ones. We derive an analytical relation that shows that the scaling exponents of transverse structure functions and velocity circulation are related in two-dimensional turbulence.