Persistence Problem in Two-Dimensional Fluid Turbulence

TL;DR

This paper investigates the persistence times in 2D fluid turbulence using the Okubo-Weiss parameter, revealing exponential decay in Eulerian measurements and power-law decay in Lagrangian vortical regions.

Contribution

It introduces a framework combining the Okubo-Weiss parameter with DNS to analyze persistence times in 2D turbulence, highlighting differences between Eulerian and Lagrangian statistics.

Findings

Eulerian persistence-time PDFs have exponential tails.

Lagrangian persistence-time PDFs in vortical regions follow a power-law with exponent ~2.9.

Distinct statistical behaviors observed between Eulerian and Lagrangian measurements.

Abstract

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter $\Lambda$ to distinguish between vortical and extensional regions. We then use a direct numerical simulation (DNS) of the two-dimensional, incompressible Navier--Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent $\theta=2.9\pm0.2$.