Universal distribution of centers and saddles in two-dimensional turbulence

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) = 1 / 4(omega(2)-sigma(2)), 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.