Towards a separation of the elements in turbulence via the analyses within MPDFT

TL;DR

This paper applies multifractal probability density function theory (MPDFT) to analyze energy dissipation PDFs from high-resolution DNS of turbulence, revealing how partial PDFs relate to the whole and enabling separation of turbulence elements.

Contribution

It introduces a novel analysis of partial PDFs in turbulence using MPDFT, demonstrating how to distinguish elements based on enstropy regions within DNS data.

Findings

Tail parts of w-PDFs can match the slope of max-PDF tails with proper magnification.

Overlap points of w-PDFs and max-PDF tails align with theoretical connection points.

Center parts of min-PDFs are well fitted by scaled w-PDFs with a common scale factor.

Abstract

The PDFs for energy dissipation rates created in a high resolution from $4096^3$ DNS for fully developed turbulence are analyzed in a high precision with the PDF derived within the formula of multifractal probability density function theory (MPDFT). MPDFT is a statistical mechanical ensemble theory constructed in order to analyze intermittent phenomena through the experimental PDFs with fat-tail. By making use of the obtained w-PDFs created from the whole of the DNS region, analyzed for the first time are the two partial PDFs, i.e., the max-PDF and the min-PDF which are, respectively, taken out from the partial DNS regions of the size $512^3$ with maximum and minimum enstropy. The main information for the partial PDFs are the following. One can find a w-PDF whose tail part can adjust the slope of the tail-part of a max-PDF with appropriate magnification factor. The value of the point at which the w-PDF multiplied by the magnification factor starts to overlap the tail part of the max-PDF coincides with the value of the connection point for the theoretical w-PDF. The center part of the min-PDFs can be adjusted quite accurately by the scaled w-PDFs with a common scale factor.