Intermittency in 2D soap film turbulence

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 Rλ, 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(δu(r)) at inertial scales r, (b) the kurtosis of P(∂xu), and (c) the scaling of the so-called intermittency exponent μ, 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 Rλ but show signs of becoming gaussian as Rλ increases beyond the largest values that could be reached. The kurtosis of P(δu(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 intermittency decreases as a power law in Rλ. This study suggests the need for a new look at the statistics of 2D turbulence.