Intermittency in 2D soap film turbulence

TL;DR

This study investigates how intermittency in 2D soap film turbulence varies with Reynolds number, revealing strong, scale-dependent intermittency that diminishes as Reynolds number increases, challenging existing theoretical predictions.

Contribution

It provides new quantitative measurements of intermittency in 2D turbulence across a range of Reynolds numbers, highlighting discrepancies with previous studies and suggesting a need to revisit turbulence statistics.

Findings

Intermittency is strong in both energy and enstrophy cascades.

Intermittency decreases as a power law with increasing Reynolds number.

Velocity derivatives remain non-Gaussian but trend toward Gaussian at high Reynolds numbers.

Abstract

The Reynolds number dependency of intermittency for 2D turbulence is studied in a flowing soap film. The Reynolds number used here is the Taylor microscale Reynolds number R_{\lambda}, which ranges from 20 to 800. Strong intermittency is found for both the inverse energy and direct enstrophy cascades as measured by (a) the pdf of velocity differences P(\delta u(r)) at inertial scales r, (b) the kurtosis of P(\partial_x u), and (c) the scaling of the so-called intermittency exponent \mu, which is zero if intermittency is absent. Measures (b) and (c) are quantitative, while (a) is qualitative. These measurements are in disagreement with some previous results but not all. The velocity derivatives are nongaussian at all R_{\lambda} but show signs of becoming gaussian as R_{\lambda} increases beyond the largest values that could be reached. The kurtosis of P(\delta u(r)) at various r indicates that the intermittency is scale dependent. The structure function scaling exponents also deviate strongly from the Kraichnan prediction. For the enstrophy cascade, the intermittancy decreases as a power law in R_{\lambda}. This study suggests the need for a new look at the statistics of 2D turbulence.