Regensburg 2022 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 34: Fluid Physics: Turbulence and Convection
DY 34.3: Vortrag
Mittwoch, 7. September 2022, 16:15–16:30, H19
The onset of non-Gaussian velocity gradient statistics in low-Reynolds number flows — •Maurizio Carbone1 and Michael Wilczek1,2 — 1Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany — 2Theoretical Physics I, University of Bayreuth, Universitätsstr. 30, 95447 Bayreuth, Germany
The Reynolds number prescribes the range of active scales involved in a turbulent flow. Stirring a fluid through a Gaussian forcing at vanishingly small Reynolds produces a multi-point Gaussian field, while flows at higher Reynolds exhibit non-Gaussianity, cascades, anomalous scaling and preferential alignments. Recent works (Yakhot and Donzis, Phys. Rev. Lett. 2017) showed that low-Reynolds flows exhibit features of high-Reynolds turbulence.
We address the onset of turbulent features in low-Reynolds flows by combining a perturbation theory of the full Navier-Stokes equations (Wyld, Ann. Phys. 1961) with the Lagrangian modelling of velocity gradients along fluid particle trajectories (Meneveau, Annu. Rev. Fluid Mech. 2011). We construct a stochastic model for the velocity gradient in which all the model coefficients follow directly from the Navier-Stokes equations. The associated Fokker-Planck equation for the single-time velocity gradient probability density admits analytic solutions which show the onset of non-Gaussianity: skewness, intermittency and preferential alignments arise in the gradients statistics as the Reynolds number increases. The results are in excellent agreement with direct numerical simulations of low-Reynolds flows.