An objective version of the Rortex vector for vortex identification

Abstract

Vortices are a ubiquitous natural phenomenon, and their structure, shape, and characteristics should be independent of the observer, which implies that the vortex identification method or vortex definition should maintain its objectivity. Currently, most of the vortex identification methods rely on velocity gradient tensors. The calculation of the velocity gradient tensor is based on the reference frame of the observer, and the velocity gradient tensor will vary with the observer’s motion. By these vortex identification methods, very different vortex structures could be visualized and described in a moving reference frame. Recently, a mathematical definition of the Rortex vortex vector was proposed to represent the local fluid rotation. The definition used velocity gradient tensor to derive the local rigid rotation axis and strength. However, the original definition of the Rortex vector is nonobjective. In order to obtain the objectivity, in this paper, by a definition of a net velocity gradient tensor, an objective Rortex vortex vector is defined which uses a spatially averaged vorticity to offset the impact of the motion frame. Some typical numerical examples, such as an implicit large-eddy simulation result for shock and boundary layer interaction and a direct numerical simulation for boundary layer transition, are provided to show the objectivity of the developed method.

Can vortex criteria be objectivized?

“…We conclude from Theorem 3.2 that a global observer change exists that is equivalent to the replacement of the with defined in (4.16) in any local vortex criterion, including the rortex criterion of Liu et al. (2019 a ). Indeed, the global Euclidean observer change exists and justifies the objectivization principle of Liu et al.…”

“…(2018), Liu et al. (2019 a , b ), Günther & Theisel (2020) and Rojo & Günther (2020). In these references, the transformation is constructed pointwise in from local, linear observer changes prescribed as For instance, the prescribed Jacobian field field may be a time-dependent rotation tensor field that makes locally as steady as possible (Günther et al.…”

“…Furthermore, despite the spectacular visualizations they provide, available numerical implementations of the optimization problem (4.12) suffer from physical and mathematical inconsistencies. Liu et al (2019a) propose to objectivize the vortex (or rortex) criterion of Tian et al (2018) by replacing the velocity gradient ∇v = S + W in the computation of Q and r min with the modified velocity gradient tensor…”

“…Different rotating observers applying these criteria in their own frames will identify different physical regions as vortices using the fluid velocity field of experiment in figure 1 in their own frames. This discrepancy between frame-dependent results from local vortex criteria and frame-indifferent results from experimental observations has prompted several authors to propose objective modifications to these criteria (Martins et al 2016;Günther, Gross & Theisel 2017;Hadwiger et al 2018;Liu, Gao & Liu 2019a;Liu et al 2019b;Günther & Theisel 2020;Rojo & Günther 2020). Some of these objectivization procedures involve the formal replacement of the spin tensor with other tensors in the original criteria.…”

Stretching and Shearing Contamination Analysis for Liutex and Other Vortex Identification Methods

“…According to Liu et al [7] , the Liutex method, Liutex-Omega method (Liu et al, 2018) [16] , Liutex Core Line method, and other Liutex-based methods ; Liu et al, 2019) [30][31][32] are the third generation (3G) of vortex identification methods. The Liutex method is discussed briefly in section 2.6.…”