Stretching and shearing contamination analysis for Liutex and other vortex identification methods

Abstract

The newly developed vortex-identification method, Liutex, has provided a new systematic description of the local fluid rotation, which includes scalar, vector, and tensor forms. However, the advantages of Liutex over the other widely used vortex-identification methods such as Q, ∆, λ2, and λci have not been realized. These traditional methods count on shearing and stretching as a part of vortex strength. But, in the real flow, shearing and stretching do not contribute to fluid rotation. In this paper, the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness. Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations. The results show that the Liutex method is the only method that is not affected by either stretching or shear, as it represents only the local fluid rigid rotation. These results provide supporting evidence that Liutex is the superior method over others.

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

“…Although the scalar -criterion identifies general rotational structures, it does not isolate rigid-body rotation from shear (Gao & Liu 2018; Shrestha et al. 2021), nor does it provide the orientation of vortical structures.…”

“…In the shear-driven flows of interest in this paper, it is meaningful to define vortical structures after an appropriate treatment of the ‘contaminating’ shear (Shrestha et al. 2021). To distinguish rigid-body rotation from straining motions, various decomposition based on the velocity gradient tensor have been proposed (Kolář 2007; Li, Zhang & He 2014; Gao & Liu 2018; Keylock 2018; Nagata et al.…”

“…Shrestha et al. 2021) is referred to as the ‘liutex’ vector, however we use the term ‘rortex’ (as originally proposed by Liu et al. (2018) to emphasise its rotational nature.…”

“…in a nearly parallel layer of vorticity not caused by a solid wall, and that embeds a density interface), such as streamwise or quasi-streamwise vortices (Schowalter, Van Atta & Lasheras 1994;Caulfield & Peltier 2000), spanwise vortices (Salehipour, Peltier & Mashayek 2015) and hairpin vortices (Smyth & Winters 2003;Watanabe et al 2019). In the shear-driven flows of interest in this paper, it is meaningful to define vortical structures after an appropriate treatment of the 'contaminating' shear (Shrestha et al 2021). To distinguish rigid-body rotation from straining motions, various decomposition based on the velocity gradient tensor have been proposed (Kolář 2007;Li, Zhang & He 2014;Keylock 2018;Nagata et al 2020;Watanabe, Tanaka & Nagata 2020;Hayashi, Watanabe & Nagata 2021).…”

Influence of Upstream Disturbances on the Vortex Structure of Francis Turbine Based on the Criteria of Identification of Various Vortexes

“…Although second-generation criteria, such as ∆ [16], Q [17], λ 2 [18], and λ ci [19] criteria, have been able to judge the presence of the local rotational motion to some extent, these methods need to adjust the threshold to accurately visualize the iso-surface plot. Dong and Liu [20][21][22][23][24] proposed a more precise definition of the vortex and vortex vector based on the DNS method called Liutex. The method combines vorticity conservation law and the vorticity transport equation to analyze the correlation between vorticity and rotation and mode decomposition and to describe the vortex structure in the flow field on the basis of the Liutex line, the Liutex iso-surface, and the Liutex vector field.…”