Universal Distribution of Centers and Saddles in Two-Dimensional Turbulence

Abstract

The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant \Lambda(x,y) = (\omega^2 - \sigma^2)/4, where \omega (x,y) is the local vorticity and \sigma (x,y) is the local strain rate. For turbulent flows driven by different external force configurations, P(\Lambda) is found to be a universal function when rescaled using the turbulent intensity. A simple model that agrees with the measured functional form of P(\Lambda) is constructed using the assumption that the stream function, \psi(x,y), is a Gaussian random field.