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DY: Fachverband Dynamik und Statistische Physik

DY 4: Fluid Physics and Turbulence

DY 4.2: Talk

Monday, March 18, 2024, 10:00–10:15, BH-N 128

Statistical modeling of Burgers turbulence with a superposition of characteristic functionals — •Gabriel B Apolinário and Michael Wilczek — Theoretical Physics I, University of Bayreuth, Universitätsstr. 30, 95447 Bayreuth, Germany

We study an ensemble of random fields, each with statistics described by a general characteristic functional. The typical length scale of these fields is a random variable and is used to model intermittency. This ensemble decomposition approach [Wilczek, New J. Phys. 18, 125009 (2016)] allows for an analytically tractable approximation to turbulent statistics, and is applied to the Burgers equation. By choosing smooth correlation functions and an appropriate distribution for the typical length scale, we build a description of Burgers turbulence at an infinite Reynolds number, in which the velocity statistics are Gaussian, but increment and gradient statistics are bifractal. Skewness, a hallmark of turbulent fields, is obtained by truncating a Taylor-expanded cumulant generating functional, and this is shown to be a useful approximation.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101001081).

Keywords: burgers turbulence; multifractal; characteristic functional; intermittency