An objective perspective for classic flow classification criteria

TL;DR

This paper evaluates classic flow classification criteria and introduces objective, frame-invariant versions using effective vorticity, applied to complex flows to enhance kinematic analysis.

Contribution

It develops objective flow classification criteria replacing non-invariant vorticity with effective vorticity, improving flow analysis robustness.

Findings

Objective criteria provide richer flow kinematic information.

Objective criteria are consistent across reference frames.

Application to complex flows demonstrates improved classification.

Abstract

Four classic criteria used to the classification of complex flows are discussed here. These criteria are useful to identify regions of the flow related to shear, elongation or rigid-body motion. These usual criteria, namely $Q$, $\Delta$, $\lambda_{2}$ and $\lambda_{cr}/\lambda_{ci}$, use the fluid's rate-of-rotation tensor, which is known to vary with respect to a reference frame. The advantages of using objective (invariant with respect to a general transformation on the reference frame) criteria are discussed in the present work. In this connection, we construct versions of classic criteria replacing standard vorticity, a non-objective quantity, by effective vorticity, a rate of rotation tensor with respect to the angular velocity of the eigenvectors of the strain rate tensor. The classic criteria and their corresponding objective versions are applied to classify two complex flows: the transient ABC flow and the flow through the abrupt 4:1 contraction. It is shown that the objective versions of the criteria provide richer information on the kinematics of the flow