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 Λ (x, y) = 1/4(ω² − σ²), where ω(x, y) is the local vorticity and σ (x, y) is the local strain rate. For turbulent flows driven by different external force configurations, P (Λ) 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 (Λ) is constructed using the assumption that the stream function, Ψ(x, y), is a Gaussian random field.