Towards improved turbulence modeling: Statistical analysis of Liutex and Liutex-based subgrid models for large eddy simulation

Vortices play a fundamental role in fluid dynamics, but mathematically defining them remains elusive. While many vortex identification methods are scalar-valued, vortices are inherently rotational, vector-based phenomena. Liutex, as a vector quantity, addresses these limitations by accurately capturing the local rotational characteristics of fluid elements while remaining independent of shear influences. This unique property makes Liutex particularly well-suited for vortex identification and the quantitative analysis of turbulent flows. This paper explores the statistical analysis of Liutex in various turbulence regimes and proposes an objective Liutex-based vortex identification method. The objective method is rooted in the statistical properties of Liutex. Furthermore, the paper investigates the performance of Liutex-based subgrid models in large eddy simulation (LES). The effectiveness of these models is evaluated by comparing their performance in different flow conditions, such as decaying homogeneous isotropic turbulence and turbulent channel flows, against conventional models. Results demonstrate that the inclusion of Liutex significantly enhances the ability of subgrid models to accurately capture flow structures. Importantly, the new model maintains the same form regardless of whether strong or weak shear is present, ensuring robustness and consistency in both vortex identification and turbulence modeling. These findings highlight the significant potential of Liutex to improve turbulence modeling in both theoretical and practical contexts, with ongoing research aimed at further refining its theoretical foundations and expanding its application in more complex flow scenarios.