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DY: Fachverband Dynamik und Statistische Physik
DY 5: Machine Learning in Dynamics and Statistical Physics I
DY 5.7: Talk
Monday, March 18, 2024, 11:00–11:15, BH-N 243
Systematic construction of velocity gradient models for turbulence — Maurizio Carbone1,2, Vincent Peterhans3,2, Alexander Ecker4,2, and •Michael Wilczek1,2 — 1Theoretical Physics I, University of Bayreuth — 2Max Planck Institute for Dynamics and Self-Organization, Göttingen — 3Faculty of Physics, University of Göttingen — 4Institute of Computer Science and Campus Institute Data Science, University of Göttingen
The dynamics and statistics of small-scale turbulence can be described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling approaches. Modeling velocity gradients in turbulence requires formulating closures for nonlocal pressure contributions and viscous effects based on modeling hypotheses about the small-scale dynamics and statistics of turbulence.
Here, we discuss an alternative, data-driven approach to derive a velocity gradient model that captures given velocity gradient statistics by construction. By analyzing the velocity gradient PDF equation, we distinguish contributions to the single-time statistics from those that impact temporal correlations. We then systematically construct a closure to reproduce a given velocity gradient PDF by design. We use the `normalizing flow' machine learning approach to estimate the full eight-dimensional velocity gradient PDF from direct numerical simulation (DNS) data. Comparisons with Lagrangian velocity gradient data from DNS confirm that statistical features of small-scale turbulence statistics can be quantitatively captured by our low-dimensional dynamical model.
Keywords: turbulence; machine learning; statistical hydrodynamics