Universality of probability distributions among two-dimensional turbulent flows

We study statistical properties of two-dimensional turbulent flows. Three s ystems are considered: the Navier-Stokes equation, surface quasigeostrophic flow, and a model equation for thermal convection in the Earth's mantle. D irect numerical simulations are used to determine one-paint fluctuation pro perties. Comparative study shows universality of probability density functi ons (PDFs) across different types of flow. For instance, the PDFs for deriv atives of the advected quantity are the same for the three flows, once norm alized by the average size of fluctuations. The single-point statistics is surprisingly robust with respect to the nature of the nonlinearity.