Velocity gradient partitioning in turbulent flows

TL;DR

This paper introduces a method to decompose turbulent velocity gradients into distinct components, analyzing their contributions across different flow regimes to improve turbulence modeling.

Contribution

It presents a novel partitioning approach of velocity gradients based on tensor decomposition, applicable to various turbulent flows and useful for turbulence modeling.

Findings

Partitioning agrees with previous results in isotropic turbulence.

Near-wall turbulence is dominated by shearing effects.

Partitioning varies systematically with flow regime and Reynolds number.

Abstract

The velocity gradient tensor can be decomposed into normal straining, pure shearing and rigid rotation tensors, each with distinct symmetry and normality properties. We partition the strength of turbulent velocity gradients based on the relative contributions of these constituents in several canonical flows. These flows include forced isotropic turbulence, turbulent channels and turbulent boundary layers. For forced isotropic turbulence, the partitioning is in excellent agreement with previous results. For wall-bounded turbulence, the partitioning collapses onto the isotropic partitioning far from the wall, where the mean shearing is relatively weak. By contrast, the near-wall partitioning is dominated by shearing. Between these two regimes, the partitioning collapses well at sufficiently high friction Reynolds numbers and its variations in the buffer layer and the log-law region can be reasonably modelled as a function of the mean shearing strength. Altogether, our results highlight the expressivity and broad applicability of the velocity gradient partitioning as advantages for turbulence modelling.