# Dresden 2020 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 3: Fluid Physics of Turbulence

### DY 3.7: Vortrag

### Montag, 16. März 2020, 11:30–11:45, ZEU 118

Small-scale averaging coarse-grains passive scalar turbulence — •Tobias Bätge^{1,2} and Michael Wilczek^{1} — ^{1}Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany — ^{2}Faculty of Physics, University of Göttingen, Germany

Capturing the multi-scale dynamics of turbulent flows remains a theoretical and computational challenge. Therefore, many practical applications require a coarse-grained description, which treats the small scales effectively. How can we obtain such effective large-scale equations? Here, we address this problem at the example of a simple, one-dimensional model for the advection of a passive scalar field. Similar to the Kraichnan model, the scalar is advected by a Gaussian random field and subject to diffusion. Despite its simplicity and analytical tractability, this model shows non-trivial features such as intermittency, anomalous scaling and a dual scalar cascade. We propose that effective large-scale equations can be obtained by ensemble-averaging over the small-scale velocity fluctuations. We show that this procedure leads to an effective diffusivity reminiscent of phenomenological eddy viscosity models. To test our approach, we quantitatively compare the large-scale dynamics and statistics of fully resolved simulations with the ones obtained from our effective large-scale equation. This confirms the ability to reproduce the large scales of a fully resolved system.