Universality of probability distributions among two-dimensional turbulent flows

We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasigeostrophic flow, and a model equation for thermal convection in the Earth’s mantle. Direct numerical simulations are used to determine one-point fluctuation properties. Comparative study shows universality of probability density functions (PDFs) across different types of flow. For instance, the PDFs for derivatives of the advected quantity are the same for the three flows, once normalized by the average size of fluctuations. The single-point statistics is surprisingly robust with respect to the nature of the nonlinearity.