Universality of Probability Distributions Among Two-Dimensional Turbulent Flows

Abstract

We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasi-geostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct numerical simulations are used to determine 1-point fluctuation properties. Comparative study shows universality of probability density functions (PDFs) across different types of flow. Especially for the derivatives of the ``advected'' quantity, the shapes of the PDFs are the same for the three flows, once normalized by the average size of fluctuations. Theoretical models for the shape of PDFs are briefly discussed.

5 pages, 7 figures

References in corpus (2)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Nonsingular Surface-Quasi-Geostrophic Flow

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• Statistical Measures and Selective Decay Principle for Generalized Euler Dynamics: Formulation and Application to the Formation of Strong Fronts