A data-driven approach for 2D vorticity PDF equations by a new conditional average estimation
This work provides a data-driven closure for vorticity PDF equations in 2D turbulence, offering a new approach for turbulence modeling, though it is incremental as it builds on existing PDF frameworks.
The authors derive dimensionally reduced PDF equations for 2D vorticity in homogeneous isotropic turbulence and propose a hybrid data-driven method to estimate the conditional average, achieving good agreement with DNS data for both decaying and forced turbulence.
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.