Berlin 2024 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 32: Poster: Active Matter, Soft Matter, Fluids

DY 32.24: Poster

Mittwoch, 20. März 2024, 15:00–18:00, Poster C

A variational approach to the gradient statistics of passive scalar turbulence — •David Aderbauer, Gabriel B. Apolinário, and Michael Wilczek — Universität Bayreuth, Universitätsstr. 30, 95447 Bayreuth

Intermittent non-Gaussian statistics are a common characteristic of turbulent flows. Various approaches exist that use a superposition of Gaussian PDFs (probability density functions) to model these statistics.

This raises the question of how to systematically construct such superpositions. Here, we address this at the example of the Kraichnan model for passive scalar turbulence, which features heavy-tailed gradient statistics.

We derive the Fokker-Planck equation for the gradient PDF and construct a solution based on a superposition of Gaussian PDFs. To this effect, we develop an optimization method to iteratively determine the weight of each Gaussian in the superposition. We compare the PDF resulting from this procedure to the one directly estimated from simulation data, as well as to the stationary solution of the Fokker-Planck equation. We briefly discuss possible extensions to statistical field theories of turbulence.

Keywords: Turbulence; Statistics; Passive scalar turbulence; Fokker-Planck-Equation