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

TL;DR

This paper develops a data-driven method to solve vorticity PDF equations in 2D turbulence, using DNS data and conditional averages, showing good agreement with direct DNS evaluations.

Contribution

It introduces a hybrid data-driven approach for solving reduced vorticity PDF equations in 2D turbulence using DNS data and conditional averages.

Findings

The method accurately reproduces vorticity PDFs in DNS data.

It works for both decaying and forced homogeneous isotropic turbulence.

Good agreement with direct DNS evaluations of PDFs.

Abstract

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.