A data-driven approach for 2D vorticity PDF equations by a new conditional average estimation

Fuente: arXiv
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Main Authors: Huang, Qian, Görtz, Simon, Hollmann, Paul, Conrad, Johannes, Rohde, Christian, Oberlack, Martin
Format: Preprint
Published: 2026
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author Huang, Qian
Görtz, Simon
Hollmann, Paul
Conrad, Johannes
Rohde, Christian
Oberlack, Martin
author_facet Huang, Qian
Görtz, Simon
Hollmann, Paul
Conrad, Johannes
Rohde, Christian
Oberlack, Martin
contents We consider the statistics for the vorticity field in two-dimensional homogeneous isotropic turbulence (HIT). First, we exploit the invariance properties to derive dimensionally reduced governing equations for the one-point and two-point probability density functions (PDFs). These take the form of linear kinetic transport equations, but with an unclosed operator in terms of a conditional average. To solve the PDF equation numerically we suggest a hybrid data-driven method that relies on carefully selected samples of DNS data and a sampling estimator for the conditional average. The method is applied to DNS data for both decaying and forced HIT, demonstrating good agreement with the direct evaluation of the PDFs using the DNS data.
format Preprint
id arxiv_https___arxiv_org_abs_2604_15551
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A data-driven approach for 2D vorticity PDF equations by a new conditional average estimation
Huang, Qian
Görtz, Simon
Hollmann, Paul
Conrad, Johannes
Rohde, Christian
Oberlack, Martin
Fluid Dynamics
Numerical Analysis
We consider the statistics for the vorticity field in two-dimensional homogeneous isotropic turbulence (HIT). First, we exploit the invariance properties to derive dimensionally reduced governing equations for the one-point and two-point probability density functions (PDFs). These take the form of linear kinetic transport equations, but with an unclosed operator in terms of a conditional average. To solve the PDF equation numerically we suggest a hybrid data-driven method that relies on carefully selected samples of DNS data and a sampling estimator for the conditional average. The method is applied to DNS data for both decaying and forced HIT, demonstrating good agreement with the direct evaluation of the PDFs using the DNS data.
title A data-driven approach for 2D vorticity PDF equations by a new conditional average estimation
topic Fluid Dynamics
Numerical Analysis
url https://arxiv.org/abs/2604.15551